I'd recommend buying some snap caps and practice your trigger pull in your spare time until you can eliminate any flinch.
I'm still relatively inexperienced with handguns I think, considering I've only been into them for ~1 year. However, just some pointers from things I've learned so far. Other than of course the 4 basic firearms safety rules, the 2 most important things with handguns seem to be front sight focus, and proper trigger finger manipulation. If you train yourself to focus on the front sight, and then train yourself to ease the trigger back properly, you'll get a good jump start on most handgun beginners. Improper trigger control seems to be the number one factor in inconsistent shots. Also, learning not to focus on the target and not to look for the bullet impact on the target, but instead to focus purely on the front sight is sort of the zen moment of shooting handguns. The reason that is, is because you don't need to see where your shots are hitting, assuming you have a proper trigger pull, where your front sight is on the target when you break the shot is exactly where it will impact. There are of course many other factors involved like grip for example. Some grip methods are inherently more stable than others, though ultimately if you have a front sight focus and properly squeeze the trigger, even if your preferred grip method is a bit less stable than others, your shots are still going to hit where intended. I use the thumbs forward approach like on that Todd Jarrett video, and it's comfortable for me and VERY stable. I'd recommend buying some snap caps and practice your trigger pull in your spare time until you can eliminate any flinch.