I sympathize with you about the flinching because I developed a flinch years ago and I attribute it to shooting really heavy loads when I first started trapshooting.The thing about flinches is that once you develope one they can be really difficult to overcome.I never could and have gone the release trigger route.Believe me though,you can still flinch on release!!!I only flinch when shooting from the gun up position as in trap.When I shoot gun down as in skeet or Clays,I don't flinch.As a general rule,it's pretty hard the beat the autoloaders for soft recoil but you can soften things up a bit without spending too much.There are several effective remedies but the cheapest and easiest easiest is to use a lighter load.Trap does not really require a super fast load.I use a sub 1100 fps load with 1 ounce of shot.This load is great for any of the three trap games but I wouldn't suggest using it from the 27 yard line in a major tournment.I'm guessing that you're not a 27 yarder anyways.I'm not a 27 yarder but I have shot some respectable scores from the back line using this slow load.If you point it in the right spot,it will break targets.I've broken 50 straights on a bunch of occasions(the 100 straights avoid me like the plauge)and doubles scores of 48's and 49's.
If you're a doubles shooter you have to be certain that the light loads will cycle your gun consistently as well.
A barrel weight can increase the weight of your gun,thereby reducing felt recoil,as well as helping to improve your swing.The weight is up front so I've found the change in balance to be beneficial,especially since you can choose where to attach the weight.I've got a friend who added a weight to his 3200 skeet gun and the best skeet scores I ever shot were with this gun.I'd like to buy it from him but he's not ready to sell it yet. I'll probably have to wait until he passes on before I can get it.He's 88 so that time may come all too soon!
I've gone the whole route with my trap guns(BT-99 and Remington 3200)Forcing cones have been lenghtened,which might help you a bit,and the cost is minimal.The barrels have been overbored and the 3200 has been ported and fitted with an adjustable cheekpiece.I even got a damaged Citori Plus from an insurance adjuster and was able to adapt the recoil reduction system to my BT-99.This made a huge difference to the recoil of my gun.It would be extremely expensive if I had tried to purchase the parts but I just happened to be in the right place at the right time and it cost me nothing.With the exception of the recoil reduction system,these other modifications all helped but in each case the change was minimal.It's a case of lots of money for minimal return.I'm fortunate in that I have a gunsmith who does forcing cones for $30 and backbores barrels for $50 a barrel.At least he did when I had the work done.
Last thing may sound a bit silly but bear with me.Are you absolutely certain that the gun fits you well?I've thought I've had good fitting guns but after making a few changes I've come to realize that I had been wrong.It's easy to make small temporary changes to your stock like shimming your recoil pad to change pitch,or using moleskin on the stock to raise your cheek a little bit.An adjustable recoil pad can be used to adjust pitch,cast off,and just about any thing else.Alan Timney used to make a really good unit.Remember that shotguns are built to sort of fit a lot of people.It's hard to get one that fits you perfectly.
Oh yeah.Talk to yourself on the line.Tell yourself that you won't flinch.It does help.
Good Luck and I hope you beat that flinch.
Dave