Have to admit, I suspect flinching is a bit like being an alcoholic. They say that once sober, an individual is still an alcoholic for life, and that they constantly have to be aware of this and fight against it. Flinching ISN"T something you can just "get rid of" and then never have to worry about again. You may conquer it once, but it's always ready and waiting to come back if you give it a chance. Takes a lot of work at keeping it away. That's exactly why Ball and Dummy is so valuable, even for very experienced shooters. I agree with the cross-training aspect, too, but it needs to be done with some serious discretion. I've heard shooters say that anything that involves pulling a trigger will help, all the way around with other shooting sports. To put it delicately, that's bullshit. Some disciplines are beneficial to one another, others are neutral and some are even antagonistic. Shotguns are a great example. I shoot rifles and some pistol competitively, and I won't go NEAR a shotgun. Trap or skeet, they promote things that are completely backwards to what's needed for rifle or pistol. You focus on the target, not the sights. You slap the trigger, instead of a controlled squeeze. There's some others as well, but everything you do with them works against your rifle or pistol training, and that's really bad news. Shooting rifles won't help with your pistol shooting, and may even hurt it. Going the other way around, bullseye pistol is a HUGE asset to a rifle shooter. Trigger control and front sight focus are far, far more critical to the pistol shooter, and that carries over into your rifle shooting. You learn to control your trigger with a 1911 in your rapid fire strings, and rifles just become downright easy. USPSA shooting is another matter. You can pick up some insanely bad habits in that game, and still get away with it completely . . . until you switch back to another discipline, and then it hurts you, big time. So pay attention to what effects one sport has on the other, and don't assume that they'll all serve to benefit your overall shooting. It won't.
Spend some time playing the Ball and Dummy games, and do some offhand work. There's no other position where a flinch will be more pronounced, and show up on paper faster. You get a good trigger break down when shooting offhand, and the rest is pure gravy.