I'm going through something similar with my 9-year old son; teaching him how to shoot. What I've found that helps at the range is dry firing before any shots are sent downrange, until he gets comfortable. Then, load one round in the chamber and have him shoot that. Then two etc. If I see him start to flinch, we go back to dry firing maybe a dozen times again; making sure that he's not flinching on the dry fire shot. Then repeat, alternating dry firing and shooting live rounds. The dry firing helps to remind him how he's supposed to pull the trigger, and get the feel for it without the anticipation of the loud sound, and observe the sights.