I tried to breed one of those rare dragons, but never got any since level 15 to level 20. I tried many suggested combinations from the wiki. Any expert here please?
Unfortunately there are no guarantees as far as dragon breeding in Dragonvale and it really comes down to luck. Rare breeding may be successful on the first try and it might just as easily take until the 50th try. You can supposedly grant yourself a slightly better chance at rare breeds by using the Epic Breeding Island. With an estimated 3% chance for the Sun and Moon, it would mean that in the average case, it could reasonably take 34 attempts, but just as some people get it on the first go, others don't until the 100th. You could have been playing this game since it came out and still not have a Rainbow dragon because it's just that rare.
To figure out your chances and get an idea of how many attempts it may reasonably take you in an average case, you can check the results that other users have submitted of their experienced by checking this handy breeding database which provides information on the success rate of particular pairings in getting a specific dragon across how many attempts. Still no guarantees though. The results here seem fairly optimistic and you may just as well halve or quarter the success rate as people are far more likely to post success than failure.
Further indicated combinations that users have claimed more successful can be found here. It also states here that "If all else fails move onto another combination. Sometimes it seems like one combo will work for one person but not another."
For what it's worth, I, my wife, and two of our kids have all been playing the game (and addicted to varying degrees) over the last 3 weeks. During this time, each of us has caved in and spent $5 on gems at one point or another.
Today it occurred to me that both my wife and daughters got their first rare dragon (or multiples) within within a day of buying gems. Until today I hadn't gotten anything rare (sun, moon, rainbow or seasonal), and on a whim, I decided to try it today, so I bought $5 worth of gems. Only 6-7 breeding attempts later, I've gotten a Sakura, a Bloom, and a rare (48-hour breed).
Until today I tought that buying a few gems with real money was a bit like cheating. It's nice to accomplish with patience what others spend money for. Today though, I thought about how much we plunk down at an arcade at the boardwalk and thought why not support the game developer a bit, since it's a great game and it's free.
It wouldn't surprise me to learn that it tangibly increases your chances of breeding rare dragons. My first inclination was to think that it would be evil, but it's not much different than dropping multiple coins in a 25-cent slot machine to add prize lines.
The only I know that you can increase your chances of breeding rare dragons is by saving up/buying gems, so that you can buy the breeding island. I'm not Shure how much the breeding island affects the chances of getting a rare dragon but I'm almost 100% Shure that it increases your chances somewhat.
(New) I just found out that the chances of breeding the rainbow dragon, because most people say that the best combination is Seaweed + Firefly. But I just got a rainbow dragon with a Blazing + Mud combination. To get to the point I just read a little bit of the wiki an it says that as long as you have four different elements "for me that was fire air earth water" to have a chance at getting the rainbow dragon. Soon to come "moon & sun dragon infomation!