Flinching is a shooting problem. Recoil may exaggerate the problem, but the problem will still exist.

Rather than buy a new deer rifle, I would recommend buying a 22 LR, that closely resembles the high power you are shooting. Buy a whole bunch of ammo, and a good book on how to shoot. Then practice, practice, practice. Every now and then pick up your high power and let one fly, then go back to your 22. Tom.