Placed in a fluid flow, a flexible plate flaps spontaneously above a critical flow velocity. The resulting self-sustained vibrations of such a flag may be used to produce electrical energy and power an output electrical circuit using piezoelectric patches covering the flag that are deformed by its flapping motion (Fig. 1a). Previous work1,2 showed only moderate harvesting efficiency with a resistive output circuit, but proposed numerous directions for the improvement. In this work, we propose a numerical investigation of such a fluid-solid-electric system with inductive-resistive output circuits. The circuit connection in Fig. 1b is considered and both linear and nonlinear studies are conducted. We identified effects of such inductive output circuit on the coupled dynamics. In particular, we show that such resonant circuits lead to a destabilization of the system and a spontaneous flapping at lower fluid velocities. Also they significantly enhance the energy harvesting efficiency of the piezoelectric flag as a result of a frequency lock-in between the flag and the electrical circuit. These results suggest promising efficiency enhancements of such flow energy harvesters through the optimization of the output circuit.