I'm a flincher by nature. And I had a bad flinch a few years ago. The best advice came from this very forum, and is premised on the notion that the flinch begins (and ends) with the eyes.
Go to the range with the softest-recoiling gun you've got - a .22lr is ideal. Don't put up a target. Just aim at the backstop and watch the gun go off as you pull the trigger. Don't worry about hitting anything in particular, so long as the bullets are going someplace safe. Just watch the gun go off. See how much you can see. Can you see the slide operate? Can you see the brass eject? Can you see the muzzle flash? If you can't, you're flinching with your eyes. Keep shooting and keep watching. You're not trying to do anything but observe.
Once you start seeing things happening while the gun is going off and recoiling, direct your attention to the front sight. See if you can watch it jump/rise in recoil when the gun goes off. See if you can see the muzzle flash at the same time. Keep trying until you can watch the front sight jump up and settle back down. No goals except to see.
Once you can see the front sight rise in recoil - and not before! - you can hang a target. Use a big one. Aim at the middle. If you hit it, great... as long as you see the front sight. Shoot a bit this way. If you start losing the front sight or stop seeing the gun go off, take the target down.
Eventually, you'll notice that you're shooting fairly compact groups without that low-left trail that the flinch induces. When you get to that point, you can start aiming small, focusing on a careful trigger pull, etc. But as long as you aren't flinching with your eyes, you are unlikely to mechanically flinch. Just keep seeing and the flinch will go away.
Eventually, move up in power if that's your goal. You may have to repeat the process as you move from .22lr to 9mm, or from 9mm to .40 major. Or from .38 special to .44 magnum. The key is to see. As long as you can see the gun going off, your brain will pretty quickly correct out the flinch.
That's the advice I got. It has worked for me. If I don't shoot for several weeks, sometimes I have to repeat parts of this process, though it's faster every time. The first time through, you might spend 500 or 1,000 rounds of ammo.