As flexible electronic technologies rapidly developed with a requirement for multifunction, miniaturization, and high power density, effective thermal management has become an increasingly important issue. The oscillating heat pipe, as a promising technology, was used to dissipate high heat fluxes and had a wide range of applications. In this paper, we reported the fabrication and heat transfer performance evaluation of a polymer-based flexible oscillating heat pipe (FOHP) prepared using 3D printing technology. The 3D-printed inner surface presented excellent wettability to the working fluid, which was beneficial for the evaporation of the working fluid. Ethanol was selected as the working fluid, and the influence of the filling ratios range of 30–60% on heat transfer performance was analyzed. It was found that a 3D-printed FOHP with a filling ratio of 40% presented the best heat transfer performance with the lowest thermal resistance, and the fabricated heat pipes could be easily bent from 0° to 90°. With the best filling ratio, the thermal resistance of the FOHPs increased with larger bending angles. In addition, the 3D-printed FOHP was successfully applied for the thermal management of flexible printed circuits, and the results showed that the temperature of flexible printed circuits was kept within 72 °C, and its service life was guaranteed.