The heat transfer performance of flat-plate oscillating heat pipes (FP-OHPs) was investigated experimentally and theoretically. Two layers of channels were created by machining grooves on both sides of a copper plate in order to increase the channel number per unit volume. The channels had rectangular cross-sections with hydraulic diameters ranging from 0.762 mm to 1.389 mm. Acetone, water, diamond/acetone, gold/water, and diamond/water nanofluids were tested as working fluids. It was found that the FP-OHP’s thermal resistance depended on the power input and operating temperature. The FP-OHP charged with 0.0003 vol % gold/water nanofluids achieved a thermal resistance of 0.078 K/W while removing 560 W with a heat flux of . The thermal resistance was further decreased when the nanofluid was used as the working fluid. A mathematical model predicting the heat transfer performance was developed to predict the thermal performance of the FP-OHP. Results presented here will assist in the optimization of the FP-OHP and provide a better understanding of heat transfer mechanisms occurring in OHPs.