Flinching or anticipation is an involuntary respond of your brain and projecting is to the muscle of upper extremities. To remove it you have to train your brain not to respond, to the recoil or the sound of explosion of a gun. To this and to reach like a high master shooter. Use 22 LR caliber handgun like Ruger Mark III, Smith & Wesson Model 41, High Standard made in Hamden). Start with bench rest shooting, concentrate on trigger pull, left hand strength is 70%, right hand strength is 30%. The trigger finger is like a lady ,squeeze the trigger slowly using the tip of your finger, until it bangs (surprised shot) hold the trigger for 1-2 seconds (follow through) because the bullet is still travelling on the barrel of the gun, then release it slowly. Keep on doing this until you assume a tight group at 15 or 25 yds. Then copy this tight grouping by shooting offhand. Then if you able to do this try a higher caliber handgun copy the same tight group that your brain and muscle have learned.
By the way, concentrate on the front, front , front sight not rear sight not the target, just the front sight, conciously always think that the right thumb is not existing (right handed) while holding the gun. Long term solution.
Short term: use the high caliber handgun right away, bench rest, then offhand shooting.
Happy shooting