A recently updated version of the MARS-F code [Y. Q. Liu et al. Phys. Plasmas 7, 3681 (2000); L. Li et al. Phys. Plasmas 25, 082512 (2018); G. L. Xia et al. Nucl. Fusion 59, 126035 (2019)] is utilized to numerically investigate the plasma screening effect on the applied resonant magnetic perturbation (RMP) field, assuming various equilibrium flow models including the toroidal flow, the parallel flow and their combinations, as well the poloidal and toroidal projections of the parallel flow. A parallel equilibrium flow with uniform radial profile is found to have no effect on the plasma screening of the RMP field, due to the fact that a uniform parallel flow merely introduces a global rotational transform along the equilibrium magnetic field lines. A sheared parallel flow, however, does change the plasma screening. The poloidal projection of parallel flow weakens the plasma screening in the resistive-inertial regime. The effect on the favorable average curvature regime is found, however, to be non-monotonic. With increasing the flow speed, the poloidal projection first weakens the GGJ-screening. Further increasing the flow speed results in enhanced GGJscreening again. This non-monotonic behavior is related to the perturbed parallel shielding current, which appears also off the mode rational surface at fast flow due to additional resonances between the RMP perturbation and the sound wave continuum. These results indicate that the flow induced plasma screening to the RMP field can have complicated characteristics, which in turn can have implications on the RMP field penetration into the plasma in experiments for controlling the edge localized modes.