The flow around a pitching NACA0015 airfoil with an oscillating trailing-edge flap is experimentally investigated to characterize the influence of the flap kinematics on the development of dynamic stall. We specifically focus on the timing of the stall development and critical values of the leading-edge suction parameter as potential stall triggers. In general, static or dynamic trailing-edge flap motions strongly affect the entire lift response but preserve the characteristic evolution of the leading-edge suction parameter. The influence of the flap on the critical values of the leading-edge suction parameter and their timing is more subtle. Variations in the magnitude of the leading-edge suction are related to the instantaneous geometric effective angle of attack. A thin-airfoil theory-based model that linearly superimposes the effect of the flap on the response for a fixed flap in its neutral position correctly predicts the maximum values of the leading-edge suction parameter. The timing at which these maxima are reached corresponds to the stall delay and is dominated by the prestall temporal evolution of the effective angle of attack. Our results suggest that dynamic stall development is governed by characteristic stall delays rather than critical values of the maximum leading-edge suction parameter.