When I worked with hunters or jumpers; I would teach flying changes by cantering a figure 8 with the crossrail at the center of the 8; asking for the change in the air over the crossrail, then going to a rail on the ground, and then just empty jump standards, and finally just cueing for the change by changing the bend. I usually waited to do this exercise until the horse spontaneously offered the change - for instance, if every time you jump a line on a green horse, you do a simple change before the turn, or halt, leg yield one step to the outside and pick up the new lead, at some point when you land from a line the horse will offer the change before you ask for the simple or transition down to halt.
Many, many people attempt to teach changes too soon - the horse has to be fit, and have a good, rhythmic, clean, 3 beat canter with adequate suspension.
I never taught a soley dressage based horse to change; I know you have to be careful to maintain straightness and correct bend more strictly than on a hunter or jumper.
Just curious - I don't think flying changes appear in US based dressage tests until 3rd level? Are you working at that level in dressage, or do you just want a solid flying changed for jumping courses or gaming?