Without reading many of the other responses, which frankly seem too short to be of much benefit, I apologize if the following has already been covered.
Start the fellow with the very rifle he seems to be afraid of. The first step is a return to basic marksmanship. Check to ensure he is holding the rifle correctly, with the butt in the pocket of his shoulder. Does the rifle fit him, if not get it fixed. Does the scope extend so far rearward, that he is in danger of getting hit by it? If so get it properly adjusted.
Explain to him natural point of aim; how to acquire it, and how to check it in each of the basic field shooting positions. Explain the difference between sight picture and sight alignment. Teach him to press the trigger at a natural respiratory pause, as this is the most repeatable breath control, and does not leave the brain oxygen deprived, the heart pounding, and the lungs gasping for air like the empty lung technique, and it provides a more stable shooting platform than the full lung technique.
Get him dry firing. Go over and over the basics of marksmanship. Breath, relax, aim, slack, squeeze. He has to learn to support the rifle by stacking bones under it, rather than muscling it around. He must develop a feel for his trigger. Begin with prone. When he can dry fire with a coin balanced near the muzzle of the rifle without disturbing it, he's ready for live fire.
Begin with a few empty primed cartridges. Continue with these until he no longer jumps at the "bang". No hearing protection should be worn at this stage. Next is live fire with handloads loaded very gently, say in the case of a .250-3000 a 100 gr bullet at 1800 fps. At this stage hearing protection should be introduced. Have him shoot offhand at 10 yards. When he can handle off hand, get him to kneel, then sit, then prone. Now extend the range to 25, then to 50, then to 100. When he can shoot reasonable groups at 100, step up the velocity to say 2500. When he throws a shot wide, get him to determine what he did wrong and what he has to do to correct it. Keep hammering the basics to him so that he is so intent upon the mechanics of the shot he doesn't have time to think about recoil or noise. Once he is shooting well out to 200 yards, let him shoot with full powered ammo, and from this point on he should be cured.
Marksmanship training can go as far as he wants to take it, but once he can shoot consistently out to 200, he has pretty much beaten his flinch. The fix isn't fast, easy, or cheap, and to succeed, he must really want it. There is little point in your dedication to fixing the problem if he isn't equally involved.