Particle flow from vacuum flashover on surface of PTFE, PMMA, and PE initiated by 60-kV nanosecond pulses in self-breakdown mode is studied in this work in the range of discharge currents of 2–6 kA. The feature of this work is changing the discharge current at the constant working voltage (~60 kV). The discharge current is varied by changing a ballast resistor. The time lag between voltage application and current rise is ~12 ns for all the values of the discharge current. This lag corresponds to the stage of conductive channel formation (high-voltage stage) and depends only on working voltage of the generator. In contrast to the low-voltage experiments (~1–5 kV) with external ignition, in our case, plasma flow characteristics depend only on intrinsic properties of the breakdown. The novelty of the proposed approach is that all the measurements are carried out at high repetition rate of pulse application (30–100 Hz). We obtained the dependence of particle flow thrust, mass loss, and share of ion component on the value of the discharge current. The results show that there is a share of the ion beam, intensity of which does not depend on the discharge current. Presumably, these ions are generated at the high-voltage stage of the flashover process. The thrust is directly proportional to the charge passed through the discharge channel. It indicates that the key factor in raise of particle flow intensity is the widening of the discharge channel at higher currents. Some of the results are of practical interest for the development of high-voltage pulsed plasma thrusters.