I always find it unsettling when things that goofy hunter people or kids on fat ponies can do with ease are such crises for dressage riders. One example is flying changes. The problem stems from this—teach your horse to resolutely hold his counter lead for about three years nonstop, and it’s no wonder he things flying changes are off his menu. The solution may seem surprising, but I can provide a long list of luminaries, many with classical backgrounds, who would echo this proposal.
Teach your horse a rudimentary change as soon as you can! If your horse is halfway balanced in his canter and reasonably relaxed, when the opportunity arises, just swap him over. It can be as early as when he’s four. You don’t need collection; you don’t need simple changes first; you don’t need counter canter.
Don’t drill them. Don’t make a big deal of it. You can even do them in a two point. Just put them on your horse while he’s still young and impressionable, and then LEAVE THEM ALONE.
Go back and do all the appropriate methodical, progressively developmental exercises that the levels prescribe. Then when you do get ready to school Third Level and changes become relevant, your guy will already have a clue what you want.