Two phases in one motion
A flick looks like one movement, but it is two. A fast ballistic phase covers most of the distance, and it is pre-programmed: your brain decides how far to move before the hand starts. Then a short correction phase fine-tunes onto the target, which is the only part vision gets to influence.
That is why the quality of a flick is mostly decided before it begins. Training flicks means training the internal map between how far the target is on screen and how far the hand has to move. Every repetition with instant feedback tightens that map a little.
Wrist flick versus arm flick
Short flicks come from the wrist, long ones from the arm, and most players blend the two without thinking about it. Your cm/360 decides the mix: a faster sensitivity lets the wrist cover more of the screen, a slower one pushes more of the work to the arm.
Neither is correct on its own. Arm movements are steadier over long distances, wrist movements are quicker over short ones. What matters is that the same target distance always produces the same hand movement.
The overshoot problem
The classic missed flick goes past the target and drags back. It feels like a speed problem, and players respond by flicking harder. It is a calibration problem. The fix is to land slightly short and let the correction phase finish the job, which is faster than a full overshoot and return.
A flick also ends in a click, which is what separates it from tracking. Tracking keeps the crosshair attached to a moving target for as long as it moves. A flick is over the moment the shot goes off.
How to train it
In Flick mode targets appear at random positions, shrink, and expire if you are too slow. Expired targets count as misses, and the score is hits multiplied by accuracy, so panic-swiping at everything is punished as hard as hesitating.
The other half of flick training happens before the target appears. Good crosshair placement turns a 30 degree flick into a 2 degree adjustment, and small adjustments land far more often than big swings.