There are 2 kinds of flinching. One is a fear of recoil.
One is called target panic. Its actually caused by fear of missing (or not shooting well), and is most common in the archery world, but some riflemen shoot poorly because of target panic also.
My guess is the kid has a case of panic.
It causes unsteady crooshairs, rushing of shots, no follow through, and "jerking" not squeezing the trigger.
It is cureable, but takes time. This will go against the advice of many, but do not step down to a smaller gun.
First, make sure the boy has been through gun safety school, and has a good functional understanding of firearms. Make sure he has some good hearing protection as well.
Go to the range with some dummy rounds, as well as live ones. Load his gun with all dummy rounds except for one live one. Watch as he aims, squeezes , and executed the shot. It will become very clear what he needs to work on.
Another thing to do is have him unload his gun. Aim at a target in a normal fashion, and practice squeezing (not jerking) the trigger. Dry fire practice. After a half hour or so, he will be squeezing off smooth shots. Have him load his gun, and try to recreate that "perfect shot". If he starts flinching again, go back to dry fire practice, many prefer snap caps for this exercise.
Also simply shooting a larger target dot can calm a fella with panic down, as its easier to hit well, and will increase confidence, and confidence is needed to shoot well. As group size returns, slowly decrease target size.
I'm an archery coach part time, and a fella with severe "target panic" can see rapid improvement sometimes just in the understanding he is rushing the shot, "punching" the trigger, and understanding the anxiety he may feel over shooting poorly.
Volumes have been written on target panic, and most pertain to archery. But target panic can cause shooting as you describe with a rifle.
Be patient with the kid, and if you can't help things yourself, hire a coach for a few lessons. A shooting coach may cost a few bucks, but can reward him with a life of hitting what he aimed at. /ubbthreads/images/graemlins/grinning-smiley-003.gif