Beating the flinch.
If you ever find yourself developing a flinch or helping a new shooter overcome a bad flinch one thing you can try is shooting with your eyes closed.
At first this may seem a little silly but I ensure you it's not. Shooting a few rounds into the berm with your eyes closed can be quite a revealing and "eye opening" experience. When you shoot with your eyes open your vision can become overwhelmed with all that is happening at once. Add to that the slide recoiling in the direction of your face and the loud report of the round and you have yourself a perfectly normal natural reaction to the situation. To flinch.
To help overcome this you can grip the pistol as usual and squeeze off a round with your eyes closed. In addition to this you can also "double plug" your ears. (Meaning to use ear muffs and plugs at the same time.) Toning down the report can help a lot, particularly with centerfire pistols. Now that you have closed your eyes and double plugged you are ready to reteach yourself that the firearm is not there to hurt you. When you feel the gun recoiling in your hands your subconscious mind relearns that the gun is not there to hurt you and there is no reason to flinch.
It's very similar to someone throwing a fastball at you, if you don't have the confidence to catch the ball you're going to flinch. If you have the confidence that you can catch the ball you will simply throw the glove up and receive the ball. Confidence comes from the subconscious, you must relax and be ready to learn. Once you have trained your subconscious that it needs not flinch after the trigger press you can continue to watch your groups shrink.