Blasting erosion arc machining is a novel electrical erosion process depending on the hydrodynamic arc-breaking mechanism to achieve a reliable high-efficiency machining. In blasting erosion arc machining, the high-velocity fluid field in the discharging gap is the precondition of the mechanism to control arc plasma to efficiently remove workpiece material. Therefore, this study mainly investigates the influence of flushing holes on the fluid field distribution directly and on the machining performance indirectly. Three multi-hole solid electrodes with different types of flushing holes are designed out according to the distributing principle. The influence of their flushing holes on the fluid field is conducted by a comparison fluid simulation which demonstrates that the electrode with flushing-hole diameters decreasing gradually from the inner to the outer in the radial direction attains the best flushing velocity distribution on the workpiece surface. Furthermore, the influence of their flushing holes on the blasting erosion arc machining performance is investigated by a comparison machining experiment in order to verify the comparison results of fluid field simulation. The experimental results illustrate that these electrodes have very different machining performance when machining nickel-based high-temperature alloy GH4169 (similar to Inconel 718) under the conditions of same discharge peak current and flushing inlet pressure. The electrode with the best flushing velocity distribution rather than with the highest velocity at a particular point achieves the best machining performance of the highest material removal rate, the least relative tool wear ratio and the least surface roughness (Ra), indicating an optimized design of flushing holes in the multi-hole solid electrode.