One of the sustainability goals in the aeronautical industry includes developing cost-effective, high-performance engine components possessing complex curved geometries with excellent dimensional precision and surface quality. In this regard, several developments in wire electric discharge machining have been reported, but the influence of flushing attributes is not thoroughly investigated and is thus studied herein. The influence of four process variables, namely servo voltage, flushing pressure, nozzle diameter, and nozzle–workpiece distance, were analyzed on Inconel 718 in relation to geometrical errors (angular and radial deviations), spark gap formation, and arithmetic roughness. In this regard, thorough statistical and microscopical analyses are employed with mono- and multi-objective process optimization. The gray relational analysis affirms the reduction in the process’s limitations, validated through confirmatory experimentation results as 0.109 mm spark gap, 0.956% angular deviation, 3.49% radial deviation, and 2.2 µm surface roughness. The novel flushing mechanism improved the spark gap by 1.92%, reducing angular and radial deviations by 8.24% and 29.11%, respectively.