I'm gonna weigh in on this one more time. I have dealt with these issues quite a bit over many years.
In addition to the last post, I forgot to mention trigger pulls. Several of you have stated that you have trouble with a flinch or failure to fire on the second trigger. If a trigger pull is too strong, it will cause a flinch.
For me, if the second trigger is over about 4.5 lbs. it is suspect. I have some old doubles with the second trigger in the 7-8 pound range. They will have me practically lurching off the launch pad in one or two rounds. So, if the second trigger is causing a flinch, check the trigger pull.
Second, as I mentioned in my last post, the length of pull can cause a flinch. If you don't believe it, get one of your old doubles with a short stock (We all have some of these, eh?) and go shoot it a few rounds. You will usually end up flinching or lifting your head or both. This may be a problem with the flinch or failure to fire on the second trigger. Traditionally, length of pull on doubles is measured to the front trigger. But, if a stock is just long enough for you to the front trigger, then it is too short to the back one. On a gun with two triggers you should use a LOP that is just a bit longer than your optimum for the front trigger to butt measurement.
Finally, on the issue of release triggers. They are obviously not an option on old doubles unless you are or have some genius gunsmith available. But for modern tournament clays guns which are shot with a mounted gun they can be marvelous. It is a whole physiological thing about releasing rather than pulling. You can find articles about it if you look.
The release triggers are really quite easy to use and master and they WILL have you shooting more smoothly.
Many years ago, when I first experienced a flinch when shooting my tournament Perazzi, I went to a release. I was amazed at how easy and natural it was. I remember telling my dear old mom (God rest her) about it. I was trying to explain why it was a good idea. She stopped me and said: "It makes perfect sense to me. I know when I try to take a picture with a camera I always move the darn thing when I try to push the button. If all I had to do was let go of the button, I don't think I would have that problem." That little old lady could just sense the logic of it.
I am fortunate that I seem to be able to shoot any trigger, release-pull, pull-pull, or double. I think one reason for that is because I went to a release-pull at the first sign of a problem. I didn't wait for it to get bad.
But, if you have an issue with a flinch, try a release on your modern guns. There is a reason that a majority of the very top (especially older) trap shooters use them.
As for the old doubles, get the triggers adjusted to a fairly light crisp pull, make sure the stock is the right length and "slap" it.
Best Regards, Jake