I actually believe going double stargate is a very viable strategy. As a top ranked master Zerg player, I've faced against the double stargate build few times and when they were executed very well by capable players, I've found it to be a very potent strategy. To understand this potency, we will have to look from the Zerg's perspective in how they will deal with the strategy.
With a stargate build, your primary goals are to scout and to harass your opponent as much as possible by picking off their drones,queens and overlords to slowdown their economy so that you enable yourself a smooth transition to Robo/Twilight + expo to third or to set up a window for a timing push.
With a double stargate build, things a little bit different: You need to either be able to finish off your opponent with the build or deal considerable amount of damage to be at an equal footing with your opponent. By considerable damage here, I mean destroying the third hatch or at least killing off a large amount of queens/overlords/drones.
Sounding very all-innish, perhaps like 7-gate? Well it sorta is an all-in build. You have to recognize that gas as a resource acts as a limiting reactant in PvZ even more so than any other match ups meaning how you manage your gas can determine the outcome of the game. And guess what? Double Stargate is a very gas intensive build. If you spend all that gas and fail to deal enough damage, you won't be able to produce enough sentries/immortals to defend yourself from the inevitable roach push - you will either lose straight from the push or they will deny your third long enough so that you lose by being too far behind economically.
So, with any good all-in builds, your primary goals should be two-fold: 1)Keeping your opponent in the dark of what you are doing and 2)Executing the all-in properly.
Keeping Your Opponent In The Dark - The path to being a ninja-toss
You must not let your opponent know what you are up to. I cannot stress point hard enough, but if a capable opponent knows that you are planning to execute a very all-innish strategy, your chances of success gets drastically lowered.
Having said that, there are generally few things a Zerg player will do to guess what you are upto.
1. Overlord Saccing
Usually around 6:30 to 7:30 minutes in game clock, a Zerg player will sac an overlord to your main to check for your tech, namely Robo, Stargate and Twilight. This is normal and you mustn't allow your opponent to scout your stargates. To do that, have a single stalker scouting at the edge of your main to pick off any incoming overlords while placing your stargate as close to the corner of your main as possible.
Here's an example of how you might go about that in Cloud Kingdom:
On some maps like Shakuras Plateau, you won't be able to hide your Stargate as easily as maps like Cloud Kingdom, because Zerg can fly the overlord into the main from all directions. You have two options: Build the second stargate at a proxied location or try to anticipate the path where an overlord might fly from. Here, the diagram 1,2,3 are the possible paths which an overlord might fly from.
It's best if you can narrow down the possibilities here: If you are absolutely certain there are no overlords at the top-left side corner of the map, then you can place your patrolling stalker to the right side of your main instead of where it's shown on the map. The above diagram assumes that you don't know where an overlord might fly from. In this case, you need to assume the worst case: that the Zerg will find one and only one Stargate and you will shoot it down before it scouts the another.
Q: Isn't it bad if you let the Zerg player scout the stargate as they will be able to build queens and pop down spore crawlers?
A: It's best if you could keep Zerg completely in the dark, but as we will see from #2 of this list, a smart Zerg player will most likely put down spores and build more queens anyways, even if you keep him completely in the dark. What's important, as already mentioned multiple times, is that you don't reveal that you have two stargates.
2. Gas Timings
The second clue that a Zerg player can gather to know what you are up to is the amount of gases you take and the timings for it. Naturally, you need all four gases in order to continuously pump air units, so there's not much you can do here but there are few things that can help making yourself as conspicuous as possible: If the map allows it, chase the overlord away from your natural's geysers so that the overlords will not be able to see your gases but this unfortunately is not an option on most maps.
Don't take all four geysers way too early, as this will most likely hint the Zerg player that you are doing some sort of gas intensive all-in or cheese. Whenever I see all four geysers taken before or around 5:30 to 6:00, I basically assume that my opponent is doing either some sort of early DT cheese off expansion or double stargate even without scouting the toss's main as it doesn't make any logical sense for any other viable strategies such as playing a macro game and taking a third as you will most likely have over 1000 gas stockpiled.
Taking the third geyser on natural early and taking the fourth geyser a little bit late can help throw off your opponent. In the latter case, there are several possibilities I have to take a guess from: a standard stargate opener, sentry-heavy push, fast DT, double stargates etc.
Unit Composition: Voidrays or Phoenixes?
This is a very map dependent question because some maps are good for void rays while others are not. Slow void rays travelling across a large map when the zerg has spawned on cross position can easily give the player enough time to build mass amount of spore crawlers and queens to defend.
For such case, it is probably best to use double chronoboosts to produce as many phoenixes as possible. Your objective in this case should be to kill as many drones/overlords/queens as possible, almost completely wrecking Zerg's economy.
But when feasible, I think mixing two or three voidrays works out much better because you will be given an opportunity to destroy Zerg's third hatchery.
In short, analyze the map in advance: consider rush distance and the ease of moving your air units to next Zerg base compared to the time it takes for Zerg to move the spore crawlers from base to base.
Executing The Attack
It doesn't matter if you manage to surprise your opponent with multiple voidrays with phoenixes while he only has few anti air units to deal with it if you cannot micro them properly.
There's not much that can be said here other than micro well. In this context, this means that pulling away damaged phoenixes/void rays from Spores and picking up Queens with enough energy to transfuse.
The attack needs to be swift as well. If you pull back and forth too often because you were afraid of losing your air units, it will give Zerg enough time to come up with a countermeasure for your air units.
Micro is an aspect of the game that takes some time to improve, so best thing to do is just diligently practice microing with Phoenix as often as possible.
The best case scenario. The Zerg player would've most likely produced Mutalisks expecting a single stargate build since a dozen of mutalisks can easily outnumber small number of phoenixes. Just mass chronoboost Phoenixes, consider getting +1 air upgrade along with Anion Pulse Crystal.
Probably the more likely choice of Zerg. The fun thing about Hydras in general is that they die pretty quickly to Phoenixes as they are light armored units. Your goal then is to never let Hydras amass by consistently flying around his main and natural, picking off as many hydras as possible while at this same time harassing his expos.
Ideally speaking, if you executed the build well it shouldn't give the Zerg player enough time to have both the upgrade for energy and have enough infestors to be able to deal with the push. But in case if he does, you should always spread out your air units. Few fungals on 9 phoenixes stuck together is basically the end of the game for you. Apply the magic box technique when you move, and strive to pick off wandering infestors with phoenixes or have them waste enough energy to be able to continuously harass safely. Generally though, a capable Zerg player can land fungal growth effectively on your units so it's best to back off and try to pick off overlords around the map and harass his mineral line when the infestors aren't there to defend your drones.
A rare case but a possibility. The idea behind this one is that the Zerg Player will keep producing Roaches to destroy your natural and main faster than you can kill the roaches with your voidrays and phoenixes. This should basically leave his third vulnerable, so it should give you enough time to kill the hatch but you do need to defend the incoming push. Correct response is to build few sentries, force field your natural and buy enough time to chronoboost out multiple voidrays from your Stargates.
The Follow Ups
This option can be ideal if your opponent has overcommitted to anti-air and has virtually nothing to defend on ground. Since double stargate is a very gas committed build, you will most likely have some minerals to spare for a Zealot heavy army.
- Expand to Third and Proceed
This is assuming if you did a considerable amount of damage to Zerg's economy, so that you bought enough time to be able to defend against any possible push from Zerg. With any remaining air units, you can consistently scout around the map and his main to pick off any overlords and to check for his tech.
Contrary to what some people think about these so called space trashcans, I really believe carriers are great in PvZ. You set yourself up two stargates, most likely +1 air upgrade (which is essential if you are going carriers) and possibly even a fleet beacon if you were intending to get Anion Pulse Crystals. Of course, you want to make sure that you are mining from 6 gases, since carriers are really expensive in gas.
Any general PvZ guidelines apply here. You should always scout in advance that Zerg isn't trying to do some sort of cheese early on if you are Forge-Fast Expanding.
At anytime during the pressure, it's possible that Zerg will try to sneak in Speedlings to deal damage to your economy so Simcity accordingly.