Re: Getting rid of a flinch.
Shay,
I don't believe the "quick fixes" as in moving to a heavier recoiling rifle. Reason being, all that does is temporarily get you used to the heavier recoil for as long as you shoot it. Once you go back to the .308 you will then, after sometime, forget how the .300 wm recoiled and you will become more used to the .308 and when that occurs, your flinch may return.
A muzzle brake will work, but i also don't believe that is the correct fix. Lots of people have been shooting unbraked 308's and heavier calibers with no flinch. There is no reason why you can't do it as well.
It, as Greg stated, is a problem with misdirected concentration and focus. You are not completely relaxed, and your focus is instead of being 99% crosshairs and 1% trigger control is 50% crossshair and 50% trigger control. Those are obviously just examples, but, the point is, your concentration is not where it should be. I do believe that ad your experience increases, you will become more accustomed to you trigger and that instance, it will be more difficult for the shot to surprise you, but, that's not to say that is where you are now. Focus on the intersection of the crosshairs, and if your dry fire has produced a proper trigger control, your shot should somewhat, catch you by surprise.
The issue you may run into with dry fire is when dry firing, you know there is no recoil to expect, so your flinch disappears. When you go to the range, you are now conscious of the live round in the chamber, and your flinch returns. Do not mistake this for saying dry fire has no positive affects. I'm not saying that. What I am saying is it us a problem with your focus, concentration, and relaxation. This must be addressed.
When you get behind the rifle, you need to ensure that your position is correct, and your bipod us loaded correctly. This will reduce the felt recoil of your rifle. If you do not have a proper stock to shoulder contact, the felt recoil will increase. I have found that if I am angled behing the rifle, when the shot brakes, my rifle will recoil to the right (I'm right handed), and if i am straight behind the rifle, but do not have my bipods loaded correctly, my rifle will hop to the left. Straight back behind the rifle, bipods loaded, proper firm contact between the stock, shoulder, and cheek will reduce the felt recoil. RELAX! It's not gonna kill you
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Practice the above stated fundamentals, focus on the crosshairs not you trigger control, and fire in your NPA. I have found that when a flinch is happening, you hold your breath and tense your body in expectation of the breaking shot. Practice trying to observe your shot impact the target, call your shot, and dry fire.
Hope that helps bud......................RELAX !