What is flinch? What is trigger control? Are they the same? Or are they just two independent causes? Are they physical or mental or both? How are they minimized? I think I have very good trigger control. Perhaps spending my teen age years on a farm hand milking 12 cows twice a day had something to do with that. Flinching? Not so good. I don't think there is such a thing as zero flinch 100% of the time. The hundreds of firearm test reports I have reviewed over the years performed by self proclaimed experts nearly always show a flyer. Oh, I forgot, flyers are caused by faulty ammunition.
One affects the other and here is what you can do about it. Not originally mine but I teach it. I learned this at the USAMU during the All Army matches from then national pistol champion Bonnie Harmon.
Dry Fire, teach yourself to use both eyes, concentrating on the sights and your trigger finger.
If you hold your arm straight out in front of you and hold your thumb up can you see the striations on your thumbnail clearly using both eyes, in other words is it in focus? You are a bifocal creature, that is you have an eye on either side of your face and they will turn in to focus on that sight about 30" in front of your nose. If you can do that then both eyes should be working and you can focus on the front sight, That is the hard part and you can see well enough to shoot like a marksman.
Next step is get snap caps for the caliber of your choice and insert it into the gun.
Get a plain sheet of typing or copy paper and in the very center of the paper use a fine point pen with black ink and make a little cross with 2.5 cm horizontal and vertical lines. No larger. Fasten that paper on a horizontal surface at shoulder height in a location with good light.
Pick up your chosen handgun with the off hand and place it in your shooting hand and get a good grip. Grip it firmly like you would a handshake, not to loose, not so tight that you shake. Extend your arm so the muzzle of your gun is no more than a cm away from the paper. Focus on that front sight with both eyes. You will see that the vertical line goes straight up the middle of the sight and the horizontal line sits squarely on the top of your front sight. Your front sight should now be centered in the notch of your rear sight and level.
Now with the gun cocked, your focus entirely on the front sight you play a little mind game. Imagine the sight is one solid piece attached to the trigger. When you pull the trigger back you are trying to pull the front sight back through the center of your rear sight. If you pull, yank, anticipate, jerk, grab anything but a perfect trigger pull those lines will move away from the front sight like a seismometer detecting an earthquake.
The objective of this exercise is to get 10 perfect shots and what you will discover is that when your focus is on the sight/trigger you will have no idea when the gun goes off. That will be your good shot.
Now the fun begins, switch the gun to your left hand and start over again. You will be sweating and hurting and mad at me but I will guarantee you that the top shooters do this and this is why they are top shooters.
Now the easy part, get your two handed grip and take 10 more shots but this part is pretty redundant. The whole point of the exercise is to get your focus on the front sight while your trigger finger squeezes the trigger without disturbing your sight alignment no matter which hand or hands you are using. If you can do that you can do it standing on one leg leaning over a table shooting through a door at an oblique angle or hanging by your knees from a trapeze bar. You will not know what position you will be in when you have to shoot but sight picture and consistent trigger pull will increase your chances of hitting what you want shot. Using both eyes will aid in your sight picture.
