A 720 double is two outside crescent kicks in one jump.
It's got classic roots. No fear factor. It's a pretty safe trick overall. It looks more complicated than it really is. It feels really good. And hey, not many people bother with this trick. I love the 720 double.
Having a strong 360 kick, cheat 720 kick, and double leg will help your 720 double more than anything. The 360 kick will polish your first kick and takeoff. The cheat 720 kick will teach you to "pump" your non-kicking leg (that is, if you pump your cheat 720 kicks). The double leg, using the same takeoff as the 360 kick but requiring more force, is a good tool for training your takeoff power. You would think that the 720 kick would be a prerequisite for the 720 double, but I don't feel it has ever helped me.
Drill the crap out of the prerequisites discussed above.
Preferably you will choose to enter this move directly from the side as I do, lest you want infinite difficulty getting the second kick out...
The second kick is always the problem on the 720 double, never the first kick. The second kick is always the problem because the first kick is never quick enough. You must rush the first kick.
Rush the first kick: Get it through as quickly as possible. See if you can find a short cut! Speed! If you have to, kick chest height or something instead of head height.
When starting this move you'll probably be in the habit of throwing a prominent first kick (like a 360 kick) and then just riding that out. Do not do that here. Follow the kick and pump!
The Pump: After your first kick comes across you need to continue pulling it around. You can facilitate this by pumping with the non-kicking leg. Just knee over the non-kicking leg. This is called "pumping". Pump the non-kicker through aggressively, it can help you follow the kick quicker.
Follow the kick: It's critical that the upper body follow the kicking leg after the first pass. The best way to study the "how" and "when" of the upper body follow, is to watch the first kicking leg as it relates to the upper body while ignoring everything else. Then watch the non-kicking leg as it relates to the upper body while ignoring everything else.
Imagine if the kicking leg goes through and the upper body doesn't follow, you have a 360 kick right? It stops. And then what, you want a 720 double so you crank out the second kick right? NO! It's not gonna happen. You'll get stuck with your backside facing the target.
This isn't a 360 kick with an extra kick. It's a 720 double! If you do the three keys (rush the first kick, follow the first kick, and pump through) what will happen is your leg almost magically sticks out again as a second kick. The quicker you are and the higher you jump, the higher your second kick will be sticking out. Have fun!