Flinch is most likely caused by firing a firearm that is too much for the person at that time. Even if a person starts out on a .22LR and moves too quickly to firearms with more recoil, they can develop a flinch. Some people don't actually have a flinch but do not do follow through. Most Americans are in a hurry, and being in a hurry to see the POI is common. A common result is they do not complete the follow through due to lowering the firearm immediately after the shot to look for the POI.
I don't get the "cool" factor. Since when is a .22LR uncool because it is not a centerfire? IMO what needs to be taught is respect for firearms and how to use them properly and safely. "Cool" will come when they see their groups shrink and can cover a three to five shot group with a quarter, a nickel, a penny and then a dime. Keep targets to track their progress and it will be plenty "cool" to them. Even adults who shoot a nice group during a class will comment that target is going on their refrigerator. There are also numerous downloadable targets designed for shooting games.