The chronology below is mostly based on this video, and my own speculations:
The order of the series is as follows:
FNAF 4 (1983)
FNAF SL & 2 (1987)
FNAF 1 (1993)
FNAF 3 (2013)
FNAF 6 & UCN (late 2010s)
FNAF VR (2020)
FNAF SB (2021)
If you're just interested in the chronological order of the games, then I hope this already answer your question. But, if you're interested in the story, keep reading. I'll try, to the best of my abilities, to make the story as painless as possible.
At 1980's, Fredbear's Family Diner opens. The diner commisioned two engineers to create animatronic mascots for them. The engineers were Henry Emily (Tape Guy in FNAF 6) and William Afton (Purple Guy). They created the "springlock animatronics", which were Fredbear (Golden Freddy) and Bonnie (Springtrap). The springlock animatronics are unique, in that they are a hybrid mascot suit, which can be used by humans, and move automatically through the use of endoskeletons. The animatronics' fatal flaw, however, lies in the springlocks, in which sudden movements and moisture can cause the springlocks to come loose, and potentially damage the endoskeleton, or worse, kill someone wearing the suit. 
After the diner was opened, Henry's daughter Charlotte was murdered by William, outside of the diner. Her soul then possessed The Puppet, serving as a guardian for the souls of the children later. Henry, devastated by his daughter's death, faded from public view.
With the murder making news and sparking a criminal investigation, the owners of the diner ran off and sold their trademark to an unknown group of individuals, who then turned the franchise into a multimillion dollar company, Fazbear Entertainment, Inc. During their prime, they made several merchandise and TV shows around Fredbear, called "Fredbear & Friends", introducing a myriad of characters such as Bonnie, Chica, Foxy, and Freddy Fazbear.
- As unsafe as it seems, remember that this is the 80's, where anything goes, and safety regulations are basically ignored, or straight up non-existant. Stuff like this gets overlooked all the time back then. Also put a pin on this. This is very important.
Five Nights at Freddy's 4
After Fazbear Entertainment managed to clean the stain on their name, the company decided to re-open Fredbear's again. Then, on the first week of its grand re-opening, William Afton's youngest son (The Crying Child/Gregory ), was having a birthday party in the diner, along with his family, including his older brother Michael Afton .
The Crying Child had a phobia of animatronics, and Michael would often pull a prank on him by jumpscaring him under the bed with a Foxy mask (the gameplay of FNAF 4 is the nightmare sequence of the Crying Child).
During his birthday party at Fredbear's, Michael and his friends decided to pull one last prank on him, by lifting him up and stuffing his head into Fredbear's mouth. His tears, combined with his sporadic movement, caused Fredbear's springlocks on his head to malfunction, and chomped off the Crying Child's head. The event was later known as the Bite of '83.
The child's soul would later inhabit Fredbear.
- Unconfirmed. I only speculate because of Matpat's newest video as of the time of this writing. Thus I will only call him as "The Crying Child".
- Again, unconfirmed, but it's heavily implied that Michael was the older brother and not the younger one. Thus I will call him "Michael".
Between FNAF 4 and Sister Location
After the event, Fredbear's was closed for good, and Fazbear Entertainment took a major blow. The springlock animatronics were decommisioned and moved into a new location, "Freddy Fazbear's Pizza" (shortened as Freddy's), where their bodies were used as a template for Fazbear Entertainment's new mascot, Freddy Fazbear. The new animatronics are no longer capable of being used by humans, but the springlocks were removed entirely, making the animatronics much safer.
However, William, inspired by his son's death, saw the potential in murdering children with animatronics. Hence, he pulled some strings and effectively close off the storage room where the springlock suits were stored through multiple means, including not putting any cameras there, reprogramming the animatronics to not recognize the rooms, etc. He then used Spring Bonnie to lure children and murder them inside the storage room, then stuffed their bodies inside the animatronics. He killed a total of five children, one of them was a girl named Cassidy, who became the second soul to inhabit Fredbear. This event was known as "The Missing Children Incident". The children then possessed the animatronics, with the help from The Puppet.
In-between his time commiting his crimes, William proposed to Fazbear Entertainment of a sister company called "Afton Robotics", with a sister location called "Circus Baby's Pizza World"(shortened as Baby's), consisting of Funtime version of the current animatronics, as well as new circus-themed animatronics, such as Ballora, Balloon Boy, and Circus Baby. The sister location, however, is a front for William to create what essentially could be called "bait-and-switch" animatronics, in that they would lure children until they are alone, and shoot out a claw to pull the child inside them, killing them stealthily.
The Missing Children Incident soon went to the news, and after reports of the animatronics emitting mucus and odor from their suits causing a criminal investigation to take place, Freddy's was eventually closed. At the same time, Baby's had it's grand opening, with William's daughter Elizabeth joining in. Despite her father's repeated warnings, she approached Circus Baby, who lures her into a room and pulled Elizabeth inside her with her claws, killing her. This caused Baby's to close down on it's opening day, with the cover story that it closed down due to "gas leaks". Baby's was later changed into a rental service for birthday parties called "Circus Baby's Entertainment and Rental".
Sister Location & Five Nights at Freddy's 2
Michael, now a grown up, was told by William that her sister is "somewhere within the rental". He then proceed to take a job at the rental as a technician. During his time there, he met Baby, who revealed all about the hidden mechanics William has made to the Funtime animatronics to kill children, and revealing herself to be the one who killed Elizabeth, and now possessed her soul. She also revealed that she has combined all the animatronics in the rental with her using "The Scooper", creating Ennard. Ennard then tricks Michael into The Scooper, killing Michael and scooped his organs out so they can use him as "a suit". After a week, Michael's body began to rot, and Ennard, realized that Michael's body is no longer useful, ejected themselves from him and ran into unknown parts. Due to The Scooper injected Remnant into Michael's body, his soul preserved, and he essentially became a zombie.
At the same time, Jeremy Fitzgerald took a job at the "all-new" Freddy Fazbear's Pizza at their grand re-opening as a night guard. In-between his shifts, William killed five more children using the same tactic he used in the previous pizzeria, causing their bodies to haunt the animatronics present (again, with the help from The Puppet), and forcing Jeremy to survive five nights of his shifts at the haunted pizzeria.
The second "Missing Children Incident" soon became public, and Freddy's are doomed to another closing. Before the closing day, however, Freddy's decided to host one last birthday party. Jeremy, after working overtime for another night, was moved into day shift. He was to watch over the final birthday party when an animatronic, agitated by Jeremy's presence, bit his frontal lobe off. This was known as the "Bite of '87". 
After the incident, the pizzeria was closed for good, and all animatronics were to be decommisioned and scrapped. At the last night after the birthday party, Michael applied as the night guard at the pizzeria as "Fritz Smith", wanting to investigate his father's murders. He was then caught and fired for "tampering with the animatronics" and "odor" (due to being a zombie).
- Canonically, it is unknown who was the victim of Bite of '87. But it is heavily implied to be Jeremy, as he was moved to daytime security for the last birthday party, and the last birthday party was when the bite happened. It also makes sense that Jeremy is the one who got bitten, since he's been actively avoiding the animatronics for five nights, and the animatronics, remembering their encounters with him, would be agitated by his presence, and bit him.
Five Nights at Freddy's
A few years later, Freddy's re-opened for one last time in the old location where the first Missing Children Incident happened. Due to it's dark history and Fazbear using the same old animatronics (which were slowly withered over time), no one actually came to the pizzeria. Michael took a job as a night guard there as "Mike Schmidt".
Michael survived for five nights in the pizzeria against the five animatronics who were haunted by the spirits of the children killed by William all those years ago. There, he learned more about his father's crimes from the newspapers scattered along the pizzeria. He then decided to go for two more nights, hoping to find a way to set the childrens' soul free. Instead, he got caught tampering with the animatronics, and fired yet again for "general unprofessionalism" and "odor".
After the pizzeria failed, Freddy's finally closed down for good. On it's closing day, William, wanting to wipe out all evidence, came to the run-down building and started dismantling all of the animatronics. The childrens' souls then confronted him, causing him to panic and ran to the storage room, wearing his Spring Bonnie costume. Due to William laughing maniacally, and the moisture caused by the rain dripoing down from the roof, the springlocks went loose, and punctured William's entire body, as he dies a slow and painful death.
With the death of Springtrap, The Puppet laid the souls of the children to rest, except Cassidy, who was still vengeful and suspected that William hasn't left his body yet.
Five Nights at Freddy's 3
After the events, Fazbear Entertainment was put under criminal investigation, went bankrupt, and ceased from public view. 30 years later, an unknown company took inspiration from the horror stories involving the pizzeria, and created a haunted house based on the first pizzeria, named "Fazbear's Fright". They managed to salvage several assets from Freddy's, including the body of William Afton, now trapped inside the Spring Bonnie suit. Unknown to the company, William's soul still preserved inside his body, similar to his son 30 years ago. Hence, Springtrap was born.
Michael, hearing rumors about a haunted animatronic inside Fazbear's Frights, decided to confront it by applying as a night guard there. He then survived six nights at the haunted house, while suffering from PTSD he endured for 30 years, manifesting as Phantom Animatronics.
After the sixth night, Michael confirmed that Springtrap is indeed his father, and burned the haunted house down, attempting to finish off his father. However, William survived, and wandered off into nowhere.
Freddy Fazbear's Pizzeria Simulator & Ultimate Custom Night
At this time, Fazbear Entertainment was bought by an unknown company, and starting to work their way back up. At the same time, Henry came out from hiding. He pulled some strings, and managed to become a supervisor for Freddy's fourth pizzeria, "Freddy Fazbear's Pizza Place", which were open for purchase for a very low cost. Michael, using the money he earned from his previous job, bought the franchise pack and became the pizzeria's franchisee.
In-between their time managing the pizzeria, Michael and Henry salvaged four animatronics found in the back alley: Scrap Baby, who were kicked out of Ennard after a confrontation; Molten Freddy, the remains of Ennard with Funtime Freddy leading the troupe; Scraptrap, whose badly damaged by the fire in Fazbear's Frights; and Lefty, a robot designed to capture the still-alive Puppet, who seeked out Cassidy and Afton in order to lay them to rest.
The pizzeria was later revealed to be a trap for the four animatronics, so that Henry can gather them in one place and finish them off. After saying his goodbyes to his daughter and former friend, he then set the pizzeria on fire, destroying everyone including him and Michael, who chose to stay to set his own soul free.
Cassidy, after a long time searching, finally found Afton's soul leaving his body and dragged him into purgatory, where he would live there eternally trapped in a cycle of being killed over and over again by his own creations.
Between FNAF 6 and FNAF VR
Fazbear Entertainment has become more and more unpopular due to the events that has happened over half the century. To add insult to injury, a game developer (Scott Cawthon inserting himself) created seven video games called "Five Nights at Freddy's", based on the Missing Children Incident up to the burning of Freddy's Pizza Place. The series was a massive success, and inspired the company to "fight fire with fire", recreating all seven games into a VR game, in order to reinforce that the events are fictional and nothing more than a series of urban legends. For this, they commisioned an independent game developer company to help them create the game.
During this time, Fazbear Entertainment also built a giant mall called "Freddy Fazbear's Mega Pizzaplex" on top of the burnt down Freddy Fazbear's Pizza Place.
Vanny, a playtester, was hired to test the game. She eventually found out about the truth from a series of recordings scattered through the game from Vanessa, a former developer of the game. She revealed that hidden inside the game's codes, was a malicious code from a circuit board of an old animatronic (heavily hinted to be Springtrap's endoskeleton). This code was revealed to be a digital copy of William Afton's consciousness, named "Glitchtrap". Glitchtrap eventually managed to trap Vanny and brainwash her into being his reluctant follower, and essentially the second "Afton".
- It is heavily implied throughout Security Breach that Vanny and Vanessa are seperate entities, despite popular belief.
- This William Afton is different from the original Afton, which is currently trapped in purgatory created by Cassidy. This William is more like a clone or lingering will, rather than William himself.
Vanny eventually continued William's crimes, killing five more children (through unknown means) before turning to a homeless child named Gregory. He then hide inside the shopping mall and lived there until Vanessa, who took a job as the night guard, found out about him and tried to capture him to "keep him safe".
Meanwhile, Glitchtrap, who managed to escape the VR game, returned to his original body and became Burntrap, hacking into the Glamrock animatronics and making them hostile to Gregory, except Glamrock Freddy, who was malfunctioning and in safe mode at the time when the animatronics were hacked.
Glamrock Freddy then helped Gregory to survive six hours in the shopping mall against the hacked Glamrock animatronics, Vanessa, and Vanny. Gregory eventually managed to defeat all of the Glamrock animatronics and take their parts to be used by Freddy. Vanny and Vanessa disappeared mysteriously after the clock hits 6AM.
After 6AM, Freddy and Gregory had a feeling that something was not right, and headed back to the mall, where they located Freddy Fazbear's Pizza Place, now in a sinkhole and infested by a monstrously large animatronic called "The Blob". The Blob was actually Molten Freddy who managed to assimilate all decommisioned animatronics to himself, and essentially lose all ability to reason and became a monster. Freddy and Gregory then confronted Burntrap one last time, and defeated him by burning the pizzeria again, just like Henry did years ago. Burntrap was later shown to be alive, but was then quickly snatched by The Blob, who presumably assimilated Burntrap into him. Gregory and Freddy then escaped together, where they live together in places unknown.
And that wraps up the chronology of FNAF.
I know a lot of stuff here are not entirely accurate, but this is because the series is pretty vague with their lore to begin with, so a lot of this stuff are a combination of speculations and reading from other theories (especially from Game Theory).
Some final footnotes: I was actually conflicted whether Sister Location actually took place before or after FNAF 1, due to the Wikipedia pages stated that SL took place during 90's. However, that wouldn't explain Michael's "odor", and why he tampered with the animatronics in the 7th night during FNAF 1&2, unless he had prior knowledge that the animatronics were actually haunted.
Hope it helps. :D