Lots of shooting is the answer, there is a technique we used to use at the range that sometimes helps as well. The shooter stays at the bench or in an off hand position while a loader stands behind him with the weapon. The loader allows the shooter to fire one round at a time handing the weapon to the loader between shots. The loader puts a single round in the weapon for each shot for several shots, then one time cycles the action but does not load a round. When the shooter is ready to fire, the loader carefully observes the shooters reaction at the time the trigger is pulled. It becomes clear very rapidly just what is going on with the shooters style. After the shot with no round, you can go several rounds without a load then slip a round in to see if there is any improvement. Use a .22 or the .257 with a light load so recoil will not be a factor then slowly increase the frequency of the live rounds. If the flinch reappears, back off on the live rounds. Practice like this over a period of days or weeks can be a great help.

Coastie
"Children are tastier than Dogs or Goats and they're far easier for a Leopard to catch" Indian Magistrate Hari Prasad Tivari