The issue of flap operation during a turn specifically relates to flap retraction which usually means an immediate turn after take-off is the worst case of a climb, low speed and low level.
The problem is that flap retraction starts well below the speed for full manoeuvre protection. For example a 737 taking off with Flap 5, entering a turn at 400' would normally start to move to flap 1 at V2+15 (say 170kts) and accelerating, which means that full manoeuvre isn't available until another 20-30kts. With extension the minimum clean speed would 210kts.
Hence, the 737 FCTM recommends for an immediate turn after takeoff, to select just climb thrust and not to accelerate and retract until the turn is completed.