The quality of the flying change very much depends on the quality of canter. If your horse’s flying changes have been erratic, unbalanced, or late behind, working on the quality and balance of the canter may be a good place to start. This video with Hannah Biggs breaks down introducing and riding the flying change, and setting your horse up properly to execute a clean change.
First, she rides straight down the centerline at the canter, preparing to change direction, then rides a shoulder-in to the new direction before asking for the flying change towards the end of the centerline. Then she moves on to ask for the change straight across the diagonal. She alternates between a nice forward canter, and bringing the horse back on his hind legs, to keep the engagement between the changes.
Check it out: