Flinching is a natural nervous response or reflex to an acquired fear.
How to avoid a flinch while shooting?
First off the flinch can be timed to the systolic and diastolic cycle, or, the heart beating which understanding is primordial especially for tactical shooters, and is intensified while we inhale or we can relax it when we exhale.
Control the annoying reflex this way:
Count mentally and do the following:
ONE, hold your weapon pointing to the front and down at aprox 45 degrees below your sight level, next to you chest cavity, the trigger finger extended along the barrel.
(In a real situation, this position keeps an assailant from grabbing your sidearm, while you can use the other hand to deflect any attempt)
TWO, raise and extend your weapon, present and acquire the target, while inhaling.
THREE, while you exhale, press the trigger in a deliberate manner.
If you exhale and didn't fire your weapon inhale again in the same position and while exhaling fire your weapon.
While you practice this controlled way, something curious happens,
you'll notice the flinch appears when you are not pressing the trigger, as soon as you present your weapon
(the trigger finger twitches and the gun moves to either side), which means you are, while exercising this manner, creating a new timing, a healthy one, different of that of the flinching reflex which was "learned" inadvertently.