Please do not use the fired case. Once compressed it provides no resistance to hammer fall or firing pin, spend the few bucks and get snap caps, they are inexpensive considering they will probably last longer than you will be shooting that gun. Best way to get rid of the flinch is to put up a white card or sheet of typing paper with a cross drawn on it in a fine black pen. put the barrel of your gun, (with snap caps inserted), as close to the paper (about 1" or less), as you can without touching the paper. Top of the front sight aligned with the horizonatal line and the vertical line centeredon your front sight.
Now when you slowly squeeze the trigger imagine that the front sight is attached to the trigger and you are drawing the front sight back through the notch of your rear sight when you apply pressure to the trigger. You will be staring at that front sight with both eyeballs at the same time you are concentrating on your trigger squeeze and when the hammer goes down you will be surprised that it happened. Do this till you can do it 10 times perfectly. It will be a long day the first time. By using a fine line and standing so close any flinch, anticipation, palming, grabbing, etc. will show up as a gross movement of the sight from your perfect alignment on that cross.
Eventually the time it takes to get 10 perfect shots will decrease as you get better. On the range practice slow fire at 50 yards or on a reduced target at closer ranges and repeat the exercise only with live ammo. You will be struggling to keep that front sight moving back through the notch and your shots will come as a surprise to you and so will your new groups. When you get consistent doing that move up to time and rapid fire but don't be in a hurry to get there. It really is true that the hurrieder you go the slower you go. Speed comes with repetition, not from forcing it.