So, how to keep the brain from freaking out?
I just take the brute force approach of shooting more regularly to desensitize the brain. In addition to centered shots, sometimes I can sense when I've got my brain right, but mixing in snap caps gives me better feedback because I can see if there is less flinch or zero flinch. It sort of works for me, but I'd like to try something different.
I incorporate a ton of dummy rounds in my range days, but it's not just to catch a flinch... because honestly? If you are shooting fast multiple rounds and you hit a dummy round, the gun will move some. That doesn't mean it's a flinch. It could just be a properly timed push into the gun to keep it flat. That's why you need a good shooter/instructor to recognize the difference, although your target prior to the dummy round should tell you all you need to know.
When I'm training a flinch out of someone, I prefer to use ALL dummys in the mag, with 1 live round. That way, you are essentially playing Russian Roulette with their brain. You mix them up and load their mags, and they think every shot is going to be 'the one'. So... you are getting conscious reps under pressure that allow them to see more and build good habits. When you hit the live round, pull everything, reset, and start again. It has no value unless their brain thinks the gun is going to go bang. Remember the 4 stages of learning:
1. Unconscious Incompetence - They don't know they are flinching. This is when it's ok to use just one or two dummies in a mag full of live rounds, to SHOW THEM what is actually happening. (After they know they are flinching, this step is USELESS)
2. Conscious Incompetence - This is that phase where they finally know they are flinching, and you start working on proper habits. This is when you flip to all dummies and one live.
3. Conscious Competence - Now they are doing it properly and slowly, but like Supermoto said, they have to really concentrate to the point they are losing situational awareness. At this point start building up to a 50/50 mix of dummies to live rounds. If they start to fail, move back towards a lower ratio of live rounds.
4. Unconscious Competence - Self Explanatory. Now is the time to move on to other skills that they suck at... and start the process over again.
Also, the idea that a gun needs to 'surprise' them when it goes off is utter nonsense. Maybe... for like 5 minutes when you are first teaching someone. After that, you need to get them to the idea of 'command detonating' the gun as Dave Harrington calls it. You will never get to upper levels of shooting if you don't understand timing. I teach in this order: Anatomy (building all the foundations of controlling gun), trigger (pressing it clean and flat... even at speed), vision (knowing what alignment you need at various distances), and finally timing... which is the magic that ties it all together when you don't move gun and detonate it when you see JUST ENOUGH to accomplish given task. No more/No Less