It's going to be one of three things: the feel in your hand, the sound, or pressure on your face/eyes. Short of wearing a gas mask, the last one is going to take time and ammo to get rid of.
Now, for dealing with a flinch, I usually just throw so much 'stuff' at my shooters that they forget about the recoil and worry more about my stuff. For kicks, I double plug 'em to see if it's the sound, and then add something with each evolution. It goes like this:
First hold the trigger all the way to the rear and keep it there after the shot. Then release it just until you feel it click when the sights are back on target.
We do 5-6 evolutions of that and see what happens. If there isn't enough result, we go to "Tell me which way your sights go in recoil and we'll adjust your grip strength from there", and I watch the sights too, giving coaching as we go.
If we're still in trouble I have them call the shot without looking at the target, sometimes even having them mark it on a mini target next to them, then looking for the hole and marking that.
In short, you need enough distractions that'll teach you something to make you forget about the recoil problem and give you some other problems to solve in the mean time.
If none of that works, I put a target on the berm, walk them up to 1-2 yards range and have them burn through 2-3 mags as fast as they can, correcting fire as they go and trying to keep them all in the "A" zone. Pretty soon they can't flinch fast enough to effect the shot, and they learn not to think about the recoil so much.
Hope somethin' in there helped!
Dan