Flinching is a difficult problem to fix on one's own.
It is a technical flaw ingrained on a subconscious level.
Some of the suggestions offered here, such as dry fire and "ball & dummy" practice, are on the right track. Other suggestions, such as"just buy a .22 revolver", are ridiculous.
Yes, flinching can and will continue once learned even with a .22.
The old saying "practice makes perfect" is not entirely true. More apt is "practice makes permanent".
Bad habits once learned must be systematically worked at to correct.
You can't buy your way out of it with new toys or do a quick fix on your next range visit.
That means professional help.
To fix the problem right, you need a coach.
My suggestion is to find a good established gun club with a competitive smallbore or airgun program and seek out a good coach.
Unfortunately, we are losing gun clubs in the United States. More people go to "gun store/ranges" than are willing to join an NRA or CMP affiliated club.
This is a huge problem!
What do most people here think of when they hear "CMP"?
Chances are, "Oh, that's the place that sells cheap M1 Garands".
But, it is in fact called the "Civilian Marksmanship Program" for a reason!
Please, please, visit the CMP website at:
thecmp.org
Then, use the toolbar to get to the "find a club" page. Hopefully, you can find a nearby club. At least, explore the website resources and check out their forum and huge library of online videos.
Get involved, find a coach, and do the work.
Or not, and flinching will keep holding you back.
(I'm hoping there are at least a few folks here that got started on the right path with a good smallbore program or something similar who'll chime in!)