Does adding flaps during ground roll perform better in short-field takeoff? In most POHs, the flap configuration for short-field is usually recommended as partial flaps, for instance 10˚ for C172. 

I remember the arguments are that full flaps would reduce the acceleration rate, and in no flaps the airplane would have to accelerate to higher speed to off the ground. In either case, the ground roll distance is longer than the optimal partial-flap configurations. 

However, this assumes a fixed flap setting during ground roll. How about let the airplane accelerate to a certain speed (in zero flaps) before adding to full flaps? We could achieve best acceleration as well as best lift-off speed?
I found this answer is a good analysis.

13.3 - Obstructed-Field - Skimming versus Wheelbarrowing or Flap-Popping
&quot;Another possible procedure (which is usually not recommended) is to keep the flaps retracted until you are ready to leave the runway. Less flaps means less incidence. A big disadvantage is that “popping” the flaps like this increases your workload at a time when there are lots of other things you should be attending to. Another disadvantage is that you run the risk of extending the flaps past the takeoff position to the landing position, creating lots of drag, which is really not what you want in this situation. If your POH calls for this procedure, go ahead, but be careful. Make sure you have some sort of detent to block inadvertent over-extension.&quot;
-- John S. Denker, See How It Flies