All a flying lead change is, is a transition to canter. The fact that you are already cantering just means you have to have better timing!
So, just think about it as a canter to canter transition. Put your aid on for your new canter - sometimes a touch with a dressage whip is useful - and if he tries and gets his change, walk and pat him. Repeat only about 3-4 times per side per session, always with a walk and praise in between and he should start to get it. If he doesn't change, bring him back to walk, pick up the new lead and praise him, then walk and praise him again. If he gets too wound up - do something else for a while, then go back. Good luck!
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