The thermal efficiency limitation of the Flat-plate Micro Heat Pipe (FMHP) is a major challenge in the development of the FMHP, where the effect of wick structure and wettability on its thermal performance is studied to improve the thermal efficiency of the FMHP. In this work, a copper spiral woven mesh and copper foam Composite Wick FMHP (CW-FMHP) is designed based on the conventional Copper Foam Wick FMHP (CFW-FMHP), and its thermal performance is analyzed regarding the wick structure and internal gas–liquid two-phase flow characteristics. An oxidized copper spiral woven mesh and copper foam Composite Wick FMHP (OCW-FMHP) has been further developed through the modification of composite wick wettability. The performance tests are carried out with the thermal transfer characteristics of CW-FMHP, OCW-FMHP, and CFW-FMHP under different filling rates and different thermal powers. The experimental results show that the thermal transfer performance of CW-FMHP reaches the optimal under a liquid filling rate of 150%, where the maximum thermal power is 15.7 W, 35.3% higher than that of the CFW-FMHP under the same filling rate. Moreover, the dynamic response characteristics of the CW-FMHP are significantly improved. The thermal resistance of the CW-FMHP is 0.48 °C/W under the filling rate of 150% at the thermal power of 10 W with a reduction of 9.4% compared to the CFW-FMHP under the same condition. Furthermore, the optimal filling rate for OCW-FMHP is lower compared with the CW-FMHP. The maximum thermal power of OCW-FMHP increases to 17.8 W while the thermal resistance reduces to 0.34 °C/W under the liquid filling rate of 140%. This implies that the composite wick structure designed in this work can improve the thermal transfer performance of the FMHP, and the composite wick with wettability modification is more effective regarding both thermal resistance and maximum thermal power.