I would recommend you get something you can shoot more frequently. When I work with somebody with a noticeable flinch, we start them with a nitro piston or springer break action air rifle. This can be shot at 7 to 10 yards in the home (basement or garage) or in the yard into a pellet trap without bothering people. The practice starts with learning how to break the trigger with out flinching. We then move to breaking the trigger without flinching and keeping your eyes open and on the target. Then move to keeping the above plus maintain the crosshairs on the aim point through the whole process. And finally the above plus watching the pellet make a hole in the target. Springers and nitro piston air rifles make enough noise and have enough movement upon firing that they can used to work through a flinching.
Next we would work with a rimfire doing the same process at a range using hearing protection at 25 and again at 50 yards. Once your not flinching and maintaining sight picture with the rimfire, we move on to a light recoiling centerfire rifle like a 223, 22 Hornet, 6.5 Grendel or the like.
This process could take a few days or a few months depending upon your time commitment and severity of your flinch. I've used this process with kids through adults. Your needs may vary. Shooting a pellet gun might not makeup for practice with your hunting rifle but it damn sure is better than no practice at all.
Jay