In every riding style, flying changes are taught in a different way. In the hunters, the changes are trained and ridden very differently from how they are done in dressage. So it is important to ask what type of riding you are talking about. What works in dressage would be a mess in the hunter ring.
In dressage, the experienced well-trained trainers, don't teach a horse and rider flying changes by running him at a wall, a jump, or throwing their weight in a figure eight. They do it a totally different way. They don't teach it until the horse is already doing a lot of counter canter work. Until the horse can hang on to that counter canter lead, and do circles, serpentines, and half circles and keep his lead round the short side of the ring, and pick up either lead and canter around without any mistakes, they won't be working on the changes. They also wait until the horse really is pretty far along in his training, and has started doing collected canter, worked on being really straight, mastered shoulder in, haunches in, half pass and pirouettes. His walk canter transitions (which are also very different from in the hunters) have to be getting really good too, because as one of my trainers said, 'a flying lead change is a canter transition', and as Nancy Smith often says, 'if you can't do a walk-canter transition, you can't do a flying lead change). If the dressage horse is straight, and responds correctly to the leg, seat and rein, and if his hind legs are strong enough and quick enough, and as long as he still isn't doing a 'baby canter' where his upright and stiff on one lead and all sprawly and long on the other lead (as they say, when his leads are 'fixed'), one day, the trainer just asks for a change, the horse says, 'what, without walking?' the trainer says with his seat and leg, 'yup!' and that's it, the horse does the changes.
