In this paper, we develop a theoretical framework for a flapping-wing actuation mechanism. Driven by oscillating magnetic torque acting on the rotor, the proposed actuator operates as a forced nonlinear oscillator. The resonance of the system is achieved by using a virtual magnetic spring without any mechanical components. Analytical models of the driving torque and the wing flapping (rotor) dynamics are derived and validated by experimental measurements from a parallel study. The flapping amplitude at primary resonance is obtained by solving the dynamic equation using the method of multiple time scale. The aerodynamic lift is then calculated based on quasi-steady aerodynamic model. Finally, the developed framework is used to investigate the feasibility and performance of the proposed actuator at different scales, while we show that a lift-to-weight ratio over one can be achieved in a large domain of design parameter space.