I was definitely not planning on self teaching it just trying to find Safe drills I can do to help get good form when a coach spots me and helps me learn it for real. Any variations besides flat back in the pit?
Honestly, I don't even like flat back in the pit. If you're coming off the bar and dropping flat to your back, then you're practicing coming off the bar with no rotation -- exactly the opposite of what you do for a flyaway.
If you want to improve your flyaway (or any skill, for that matter), the best way is to break it down into its components. And in the case of a flyaway, this is pretty easy, because it is composed of two very simple components: a tap swing and a back tuck. Both of which are comparatively easy to train on your own.
A tap swing is pretty self-explanatory, but try to really focus on feeling what the bar is doing while you swing. As you come down from the back swing and approach the bottom of the swing, and do the arch-snap through the bottom, really try to feel how the bar bends. You should feel it bending down and slightly back, and then feel how it slingshots you up towards the top of the front swing. Try to notice the exact moment of that slingshot effect; it should happen right as your toes are snapping up. That moment is where you will release the bar to do your flyaway.
The second part is a back tuck, which you should train on trampoline whenever you can. I recommend training it two ways: from your feet and from a back drop. In both, pay attention to what you see; you should see the wall in front of you, see your knees coming up over top, and see the floor before you land. Usually, I favor a fairly tight tuck, with the hands on the shins; however, for a flyaway I prefer an open tuck, with the arms out to the side. Think of it as an exaggerated candlestick position, but with the knees bent.