Slapping the trigger helped me overcome it. Literally having your finger barely off the trigger and then consciously slapping it to trigger the shot. Never flinched, not even once, when I remembered to do that. It's gone now. Haven't flinched in ages. So, there's hope. Just keep trying stuff.
My flinch was definitely not recoil related. Often any changes in my routine would see me go flinch free for awhile, even going from 1 oz. loads to 1 1/8 oz. loads. But, it would always come back. Until I started slapping the trigger. I'll always believe that the type of flinch I had was more related to a fear of missing. I literally wanted to break every single target, every time.
Slapping a trigger seemed counterintuitive to me, coming from a pistol and rifle shooting background. But, I can assure you (I punched into Master class while "defeating" the flinch) that it is not detrimental to shotgunning in the least.