Sadly, the one thing that eliminates flinch in my world, has been a 20 gauge Remington 1100. A 28 gauge 1100 works, too. I say sadly because I’d prefer to shoot just about anything else.
I had flinch sneaking in when I started shooting off my right shoulder, after fifty years of shooting left handed. I discovered it the same way you did, having the trigger selector in the wrong spot to make a single trigger work on the barrel I had chosen, and the gun not going off. I have made progress, believe it or not, by practicing my mount and pulling the trigger on an empty chambers in my dinning room, with a gun that is OK to dry fire, a 12 gauge Darne.
The old proverb “Getting old ain’t for sissies” is sadly true, as well. Best of luck to you.
Best,
Ted
