Flying animals resort to fast, large-degree-of-freedom motion of flapping wings (i.e., their aerodynamic surfaces), a key feature that distinguishes them from rotary or fixed-winged robotic fliers with relatively limited motion of aerodynamic surfaces. However, it is well known that flapping-wing aerodynamics are characterised by highly unsteady and three-dimensional flows difficult to model or control. Accurate aerodynamic force predictions often rely on high-fidelity and expensive computational or experimental methods. Here, we developed a computationally efficient model that can accurately predict aerodynamic forces generated by 548 different flapping-wing motions, surpassing the predictive accuracy and generality of the existing quasi-steady models. Specifically, we trained a state-space model that dynamically mapped wing motion kinematics to aerodynamic forces and moments measured from a dynamically scaled robotic wing. This predictive model used as few as 12 states to successfully capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. Also, we provided a comprehensive assessment of the control authority of key wing kinematic variables and their linear predictability of aerodynamic forces. We found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half stroke cycle. Furthermore, the angle of attack, normal acceleration, and pitching motion had the strongest and the most instant effects on the aerodynamic force/moment generation. Our results show that flapping flight offers inherently high force control authority and predictability, which are key to the development of agile and stable aerial fliers.