Im teaching my boy to do flying changes, right now, how am I doing it, is going to be hard to explain but I hope it helps.
It is a slow process I personally don't like to push them specially cos my boy is way to green.
I start cantering arround the arena, then I do diagonal changes extending the cantering not letting him break into trot, when im in the middle of the diagonal y press my outside leg (the leg that was facing to the fences) into the ribs with a oderate pression it will be less and less as he ctahces the idea, bout you have to be very clear on your comands at the bigining, I then change sides and he will do a flying change.
Sometimes specially when they are starting they change the font but nbot the hind legs, when that happens I speed a little and canter a circle using my outside leg to ask him to change the hind legs.
Its very importat that you do not pull on teh mouth when you ask for the changes and have patience.
When my horse does it 2 times each side im done and happy, once he does it I pad him and congratulate him imediatly, if not I correct my canter and keep trying.
Good luck and I hope its clear and it helps.