The prominent maneuverability of flapping flight is enabled by rapid and significant changes in aerodynamic forces, which is a result of surprisingly subtle and precise changes of wing kinematics. The high sensitivity of aerodynamic forces to wing kinematic changes demands precise and instantaneous control of the flapping wing trajectories, especially in the presence of various types of uncertainties. In this work, we first present a dynamic model of a pair of direct-motor-driven flapping wings while taking into consideration the parameter uncertainties and external disturbances. We then present an Adaptive Robust Controller (ARC) to achieve robust performance of high-frequency (over 30Hz) instantaneous wing trajectory tracking with onboard feedback. The proposed control algorithm was experimentally validated on a 7.5 gram flapping-wing MAV which showed excellent tracking of various wing trajectories with different amplitude, bias, frequency, and split-cycles. Experimental results on various model wings demonstrated that the ARC can adapt to unknown parameters and show no performance degradation across wings of different geometries. The results of ARC were also compared with those of open-loop and classical PID controllers.