In a system where wind farms are connected to the grid via a bipolar flexible DC transmission, the occurrence of a short-time fault at one of the poles results in the active power emitted by the wind farm being transmitted through the non-faulty pole. This condition leads to an overcurrent in the DC system, thereby causing the wind turbine to disconnect from the grid. Addressing this issue, this paper presents a novel coordinated fault ride-through strategy for flexible DC transmission systems and wind farms, which eliminates the need for additional communication equipment. The proposed strategy leverages the power characteristics of the doubly fed induction generator (DFIG) under different terminal voltage conditions. By considering the safety constraints of both the wind turbine and the DC system, as well as optimizing the active power output during wind farm faults, the strategy establishes guidelines for the wind farm bus voltage and the crowbar switch signal. Moreover, it harnesses the power regulation capability of the DFIG rotor-side crowbar circuit to enable fault ride-through in the presence of single-pole short-time faults in the DC system. Simulation results demonstrate that the proposed coordinated control strategy effectively mitigates overcurrent in the non-faulty pole of flexible DC transmission during fault conditions.