Nathan,
Yup, there's more than one way to develop the skill of pressing a trigger quickly while keeping your sights lined up. And that's a reasonable one.
But once someone has
already developed a flinch, it's faster in the long run to slow them down on the trigger press, let them learn it in slow motion, and then bring them back up to speed. A guy or gal who's already flinching, if you tell them to move the trigger quickly, they're just going to flinch more and embed the core problem more deeply.
Here's the process I recommend for bringing someone's slow trigger press up to speed without losing the basic skill set:
The Speed Up Drill.
There's another cool drill I like to do for quick accuracy without a flinch. Requires either a friend or a random-start buzzer to give you a signal, though. Put your target close enough that you can easily shoot one ragged hole. Get your sights on target with your finger resting on the trigger, ready to shoot. As soon as you get the signal,
immediately press the trigger. (This one works really well with dummy-and-ball loading, btw.) Do it repeatedly in dry fire, then go live until the flinch comes back. The moment the flinch comes back, move back to dry fire for at least 10 reps, more if the muzzle dips. Keep going back and forth between dry and live, gradually increasing the number of live reps, until you can always keep on target with a quick press the moment the signal goes.
pax