I think your shooting goals will have a lot to do with the kind of advice you need to hear. Are you trying to shoot slowfire bullseye groups, or are you shooting for "practical accuracy" (at, say, an 8" target), rapidly? For perspective, I do the latter.
What you have to do to make the bullet hit the target is see the target, put the sights on the target, and pull the trigger without disturbing the sight alignment badly enough to miss whatever target you are shooting at. If the bullet doesn't hit the target, you didn't accomplish one of these three things, even if you think you did.
Different thought processes work for different people I guess, but personally I've always been completely dumbfounded by some of the very common advice on how to accomplish the above. Just some examples:
1) "Balance a (coin, case, whatever) on the muzzle and pull the trigger." I'll be the first to tell you I couldn't balance any solid object on the muzzle, with or without a trigger pull.
2) "Be surprised by the trigger break". After about 10 pulls of a new trigger, never mind 10,000, I have a pretty good idea of where the trigger breaks, and there are few surprises going forward. I like to keep surprises to a minimum.
3) "You are pushing/slapping/jerking/punching/caressing/whatever else" people are said to be doing to a trigger to knock the sights out of alignment during the trigger pull. I sometimes wonder if the verb of the day even means anything to the person dispensing the advice. I assume these are all ways of getting at the same concept; pull the trigger without moving the gun. I sometimes wonder if we sat around coming up with the most complicated ways possible to articulate this.
Dryfire has been excellent for me recently, mostly for operations that don't actually involve a bang, such as drawing, reloading, indexing/seeing the sights, etc. But also, you can see the "follow through" of your trigger pull that is interrupted by recoil when ammo is present. That is, if you are regularly doing something that moves the gun as part of your current trigger pull mechanics, the sights will tell the tale during dryfire. We all "flinch", or "anticipate recoil" to some degree. Usually the faster we are shooting the worse it gets. But if your fundamental mechanics are sound, you should be able to cancel this out by taking as much time as you need to execute a perfect trigger pull in slowfire and shoot a tight group. If you can't do that, there is something about your trigger pull that is disturbing the gun/sights. If you can, it is just a matter of getting the proccess sped up after that, if that is your goal, and there isn't much besides practice that will do that.
I also try to use a very firm grip with my support hand. Not only does this help control muzzle rise and keep the gun from moving in your hand, it has the effect (for me at least) of partially decoupling the control of the gun from the hand that is pulling the trigger. I personally believe that most of our "flinching" comes from the trigger pulling hand, and thus the more control we can transfer away from this hand, the less "flinch" will become a factor. This is a personal observation that you may or may not concur with over time.