Flinching can only really be corrected by proper instruction-my experience is that, if you go from a low to a high caliber, they will still flinch-not the first shot, but every one after that. And, going from high to low caliber, the same thing happens initially-you compensate for the expected kick. Even experienced shooters do this-maybe not to the extent that other would, but, it does happen. Your body simply gets used to one thing, and reacts the same in a similar condition ( the rifle or pistol doesnt change, just the caliber).
Shooting .22 conversion kits do have benefits though-primarily, its a cheap way to shoot! But, you will not get the same ballistics as a full powered round. The basics will be the same, yes-but shot placement will be completely different. But, you can practice mechanics, VERY cheaply-offhand shooting, transition drills, reloads, malfunctions, and, well, you just plain get to be a lead farmer . Nothing wrong with a day at the range!