A nonlinear energy harvesting system consisting of a flapping foil and an electro-magnetic generator excited by incompressible quasi-steady air flows is investigated. Due to stiffness nonlinearities in pitch and/or heave degrees of freedom, the system behaves a stable limit cycle oscillation when flow velocity exceeds the critical flutter speed, so that the mechanical energy imported from air flow is converted into electricity by the coupled electro-magnetic generator. The power flow equations and variables, including the input, dissipated, transmitted and harnessed powers, of the system are formulated. A fourth-order Runge-Kutta method is used to obtain the system's dynamical response as well as power flow variables. It shows that increasing the nonlinear stiffness in heave motion or decreasing in pitch motion benefits power generation. The research demonstrates the capability of this nonlinear system to harvest natural energy without extra operation cost. Discussions and planed further research works are given for engineering applications.