Aeroelastic instabilities have been frequently exploited for energy harvesting purpose to power standalone electronic systems, such as wireless sensors. Meanwhile, various energy harvesting interface circuits, such as synchronized charge extraction (SCE) and synchronized switching harvesting on inductor (SSHI), have been widely pursued in the literature for efficiency enhancement of energy harvesting from existing base vibrations. These interfaces, however, have not been applied for aeroelastic energy harvesting. This paper investigates the feasibility of the SCE interface in galloping-based piezoelectric energy harvesting, with a focus on its benefit for performance improvement and influence on the galloping dynamics in different electromechanical coupling regimes. A galloping-based piezoelectric energy harvester (GPEH) is prototyped with an aluminum cantilever bonded with a piezoelectric sheet. Wind tunnel test is conducted with a simple electrical interface composed of a resistive load. Circuit simulation is performed with equivalent circuit representation of the GPEH system and confirmed by experimental results. Consequently, a self-powered SCE interface is implemented with the capability of self peak-detecting and switching. Circuit simulation for various electromechanical coupling cases shows that the harvested power with SCE interface for GPEH is independent of the electrical load, similar to that for a vibration-based piezoelectric energy harvester (VPEH). The SCE interface outperforms the standard interface if the electromechanical coupling is weak, and requires much less piezoelectric material to achieve the maximum power output. Moreover, influence of electromechanical coupling on the dynamics of GPEH with SCE is found sensitive to the wind speed.