The Power flow controller (PFC) is a key element for meshed DC micro-grids. Indeed, this device is able to balance the electric power between the lines of a node in the mesh, which is required to maintain the stability and prevent the overloading of some lines. This paper presents a differential flatness based nonlinear control for this device. The chosen converter topology is modelled by a modular state-space nonlinear system. The primary control objective is to achieve power control on the line connected to each terminal of the PFC despite the uncertainty of the grid. The considered PFC is equipped with a reservoir capacitor. Voltage regulation of this capacitor is also addressed, as a secondary control objective. Simulation results for a 3terminal PFC show the effectiveness of the proposed control. The extension to a 5-terminal PFC demonstrates that the control for an m-terminal PFC is easily implemented thanks to the modular structure of the proposed control scheme.