I know you probably know most of this, however, I think you may benefit from going over this information again. I wrote this up for one user on here asking a question about Flying Lead Changes and it covers a lot of good information. I hope you enjoy!
First of all a horse should be picking up the correct and counter lead when asked 100% of the time and should be able to perform simple lead changes before even attempting a flying lead change. Sure, you might get lucky and accomplish it, but it will be far from correct. Anyway, the horse and rider should be balanced at the walk, trot, canter and should have mastered basic to advanced body control. When I say this I mean the horse willingly moves his shoulders, ribs, and hips. He should also understand vertical and lateral flexion as well as how to bend his body. Not to mention must grasp the concept of rounding the back and driving underneath themselves with the hindquarters (aka collection). Sound simple? Think again for this is merely the foundation that equestrians use to build a flawless flying or interrupted lead change.
You must also understand the rhythm of a canter. The correct execution of his gait is three beats. Next time you watch a horse canter or lope, take a close look at how his legs move. When transitioning into the canter going to the left the horse first strikes off with the right hind hoof, then the left hind and the right fore move in unison, and lastly the left fore finishes the stride (and this is your left lead). When going to the right the horse's left hind hoof begins the stride, followed by the right hind and left fore moving in unison, then lastly the right fore finishing the stride (hence your right read). So in reality the canter starts in the hindquarters then finishes with your correct lead.
Make sense?
Before you can think about a flying lead change you must understand the biomechanics of the horse and what it takes to reach that level of performance. Without this you will find your horse picking up wrong leads, cross-cantering, and not picking up the leads correctly on all four legs. I could continue rambling on, but it's getting late so I'm afraid I'm going to sum up leads in a nut shell.
It's all about hip control. Think back on how all of your canter departures start on that hind left or right hoof. If I shift my horse's hip to the left and squeeze my right leg he is prepared to pick up the left lead. If I shift my horse's hip to the right and squeeze with the left leg he is prepared to pick up the right lead. When you squeeze your leg against the side you are not just asking for impulsion to the canter. You are actually asking for your horse to tilt his hip towards the inside of the arena AND then DRIVE that outside hind to pick up the inside lead.
If you horse is cross-cantering it's because more than likely he switched in the front but not in the hindquarters. So although you may of asked him to swing his hindquarters in, he may of gotten lazy and tried to avoid it. So start working on getting him to bend his hip to the inside and outside of the circle. He should nail those flying lead changes because you're setting his body up to change at the same time.
Remember don't get in a rush, or else you'll skip steps. Training horses and riders is like building a house... first you have to pour the cement and lay a foundation before you can start building up to the more complex stuff.