Mobile energy storage (MES) could effectively support power supply security of distribution network. In this paper, a coupled spatiotemporal coupling model of mobile energy storage regarding its energy regulation, moving location and accessed points to distribution grid is first established; then a two-stage optimal energy dispatch strategy of distribution networks considering the operation flexibility of MES is proposed. In the first stage, the location of MES and optimal output of distributed generators are pre-configured before the fault, achieving the minimum load shedding penalty of distribution network; in the second stage, MES accessed points and the corresponding charging/discharging power, as well as the active and reactive power of distributed generators are collaboratively optimized to achieve the minimum operation cost of distribution network. Finally, the effectiveness of the proposed two-stage optimal operation strategy of distribution networks considering MES Flexibility was verified by the IEEE 33-bus network.