Well, a flinch is common, in fact, I think that most shooters have a flinch to some degree.
Here are a couple of things I do to overcome it: (Many of which I learned here...)
1. Dry Fire!!!
UNLOAD GUN! REMOVE AMMO FROM ROOM! CHECK AGAIN!!!
Once you have determined that no loud noises will exit your barrel, set up your dry fire target. My "Time" picture of Bin Laden has come in handy for this. (You want a dedicated dry-fire target that youput up when you start, and take down when you are done. You don't want to pick something like a light switch or doorknob. I guess that some people have "finished" dry-firing, loaded back up, and then decided to try it "one more time". By having a target that you take down after the session, you minimize the risk of total brain fade.)
Anyway, set up target, align sights, and press/squeeze the trigger. What you want is to be able to drop the hammer without your sights moving at all. Do this every day for ~15 minutes and your trigger control/muscle memory will improve greatly.
If you pull a shot and your sights move, then stop, take a deep breath, call your shot (tell yourself something like "My shot was low and to the left")and get back to basics---Sight picture, sight alignment, and trigger control.
2. The "Ball and Dummy" drill
This works best with a friend.
Take some dummy rounds (snap caps) with you to the range--Have your friend load your magazines while you aren't looking (Or dump your ammo on a table with a few dummies, and load your mags with your eyes closed)and get ready to shoot.
Concentrate on the fundamentals, Sight picture, sight alignment, and trigger control, and go shoot.
Sometime during that shooting, the dummy round will chamber, and your gun will go "click" instead of "Boom". Did the gun move? If it did, you are anticipating the recoil and flinching. Stop, take a deep breath, and tell yourself to go back to basics.
Flinch is a mental thing. The more you think about and fear the recoil, the more you will flinch. The key is to overcome the fear through experience and proper technique. If you perform these two dills on a regular basis, you will improve dramatically.
Get a .22 or a .22 conversion kit for your 1911 or other gun! Ammo is cheap, there isn't much recoil, and the grip/trigger pull is identical. I bought the Wilson .22 conversion kit and it has been reliable, accurate, and a ton of fun to shoot!!!
I agree with Bill. I used to flinch a lot. Lots of dry fire helped fix that problem. If I found myself flinching at the range, I pulled the mag and dry fired 10 or 15 times before resuming. I never tried the snap cap idea, but I'm sure that would be a great exercise. Dry fire alot at home and try to relax. I always remove the mag and clear the chamber before dry fire practice at home and I always put my mags and ammo far from where I practice. Think about the sight picture and not the bang.
I agree with adding a dummy round or two. When the dummy comes up (you shouldn't know when) it will allow you to see how your sights react to your trigger pull. If the gun goes click but the sights jump off the target, you're still flinching. Practice at the range dry firing at a target and load up and try to duplicate the dry firing process with live rounds. I don't feel that the dummy round in the mag actually helps cure the problem but it will help you notice that it is happening.
Flinching is also a symptom of lack of follow through - not holding aim & concentrating on the front sight. You need to be able to "call your shots". You should see the fire at the end of the barrel on a frequent basis.
Often it is mind over matter - like not bailing out the batter's box when a pitch starts from behind your head and ends up on the inside of the plate.
It is a natural, instinctual response, like blinking when something nears your eyes. Just like a boxer - you need to keep your eyes open. Not doing so has negative consequences in both boxing & shooting.