No, it's not a "flinch".
The Task-specific Focal Dystonia that we call a “flinch” is a 2-part event (though occurring almost instantaneously):
1st is the “trigger freeze” from involuntary and dysfunctional contraction of opposing small muscles in the hand and forearm, followed by
2nd an entertaining variety of bodily reactions; lunging, jerking, stumbling toward the trap house, etc. involving large muscles.
The reason we can't pull a pull trigger is because the extensor muscles (Extensor indicis and Extensor pollicis longus) are contracting rather than relaxing, and the flexor muscle (Flexor digitorum profundus) will not contract (that’s the short version and ignores the contribution of the Lumbricals and Interossei).
Recoil clearly contributes to flinching, but there is no recoil in putting or throwing a dart, and people still "yip" or have "dartitis"
Almost all of us push our bodies forward with recoil (obvious when we have a dud), but that is recoil compensation, not a flinch.
Recoil/noise avoidance flinching before the shot (ducking the head, closing the eyes, being unable to pull the trigger without jerking) is a physiologic response to an unpleasant stimulus, is not a task-specific focal dystonia, and one can become accustomed to the stimulus, and the response thereto attenuated.
There are visual flinches. If I'm not precise in placing the cursor arrow exactly where it needs to be, I flinch. If I cover the target with the barrel, I can flinch.
The dystonia in ‘dartitis’, archer's ‘trigger panic’, and throwing a baseball or cricket ball is failure to relax the muscles ie. inability to “let go”; the opposite of a shooter’s ‘trigger freeze’.
Moving the gun before the target appears has been called “forecasting the target” and is purposeful (though involuntary), rather than a dystonia.
I have no idea what you are doing with your trigger finger, but the cure is to become a trigger "slapper", NOT to "stage" the trigger.