A flat heat pipe is a heat transfer element with a flat shell structure on the outside and efficient heat transfer through the phase change of gas and liquid inside. To study the fluid-solid coupling and phase change heat transfer process of a flat heat pipe, a coupled heat transfer mathematical model of a flat heat pipe based on its heat transfer physical model was established. The phase change heat transfer of the fluid in the heat pipe was computed using the multi-relaxation pseudo-potential lattice Boltzmann method, and the fluid-solid coupling heat transfer process of the flat heat pipe was numerically solved using the partitioned and boundary coupled solution method. The maximum error between the simulation results of the multi-relaxation pseudo-potential lattice Boltzmann model and the theoretical model for the nucleation process of a V-shaped cavity was less than 13%, verifying the accuracy of the multi-relaxation pseudo-potential lattice Boltzmann model. The dynamic coupled heat transfer temperature field distribution law in the fluid of a flat heat pipe was obtained through simulation, providing a new theoretical method for the fluid-solid coupling and phase change heat transfer research of flat heat pipes.