if you can't control the front, middle, and back of the horse you can't get a flying lead change. Period.
If you don't have control of of your horse in its entirety, you shouldn't be doing flying changes.
a lot of people try to just ride the front or throw their weight over the get the change - this is not correct. You should not make your horses hips move over when you ask for the change,
True enough. So loosening the hips up should not be required as any sort of preparation
but you need to have control of the hip and that's why you practice being able to move them.
Since the only hip movement" done is the riders ( not the horse) this maneuver becomes unnecessary.
if you can move them back and forth you can also move them to be straight and get a correct change. Sorry if I didnt explain that well enough in the first place.
The only reason you may want to do some sort of movement like a travers, renvers would be for suppling but the NEED to do either of these movements are not necessary if you have the horse going forward and straight.
What you do need to control is the placement of the hind leg so the horse can switch the lead by causing the former inside leg to land sooner and carry more weight and the former outside travel longer and carry a lighter load...while the horse is straight and with no swing of the haunches.
I personally recommend having the horse able to carry a decent canter and COUNTER canter before trying the flying change.