Everyone may not agree with my tactics but the way I taught myself to stop flinching went as follows.

I had a buddy help me to kinda supervise.

I went out and shot 3 arrows, flinching the whole time.
Next I drank a beer.
shot 3 more arrows, still flinching
Drank another beer....

Well you see the pattern. And eventually I was relaxed enough a freight train could have come at me and I wouldn't have flinched. Then I continued to shoot as I sobered up. Haven't flinched since. I am not recommending this method for everyone. It is meerly what helped me. I will help you stay relaxed. Also note I didn't drink to the point it was unsafe to shoot. just enough to relax. And that was why I had a good friend there. To ensure I didn't get to that point. He basically cut me off when I quit flinching and it helped me.