To teach your dog to do a back flip, when the dog is in the air help it flip over backwards enough times that it starts to do it on its own.
How Do I Teach My Dog How To Do The Backflip?
Its a very difficult and dangerous process. I don't recommend it. To be able to preform a trick like that you need to exam your dogs age, weight, and breed. If you are certain your dog can handle it, then I recommend visiting a website called www.superfetch.com (or search super fetch into google.) Its a tv show where one guy teaches dogs how to preform extreme tricks. It gives you step by step directions on how to teach and preform the trick safely.
I know nothing but I can only imagine that you teach your dog to beg and once done, get him in the beg position and hold a treat higher above his head so that he has to jump to get it, and then shape it to what you want.. :)