This numerical investigation employs a two-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) approach with the k-ω SST turbulence model to systematically evaluate the impact of bleed-feed channel geometry (with three width variations: 0.2D, 0.25D, and 0.3D) on double feedback fluidic oscillator performance. The focus is on improving oscillation frequency and heat transfer while reducing pressure drop, which are critical parameters in fluidic oscillator-driven jet impingement cooling applications. Addressing these challenges is essential to enhance cooling performance, minimize energy consumption, and enable reliable thermal management in advanced engineering systems. The study analyzes key performance parameters, including oscillation frequency, pressure drop, and heat transfer characteristics, comparing channel-enhanced designs against a baseline smooth oscillator. Results demonstrate that incorporating a bleed-feed channel significantly enhances performance, with the 0.3D width emerging as optimal, delivering a 150% increase in oscillation frequency and a 3.2% reduction in pressure drop compared to the smooth design. These improvements are attributed to the channel’s ability to strengthen feedback flow, thereby accelerating jet switching while minimizing energy losses. Thermally, the 0.3D configuration achieves a 7.3% higher Nusselt number than the smooth oscillator, resulting from combined effects of higher oscillation frequency (intensifying boundary layer disruption) and increased jet momentum from reinforced feedback flow. The progressive performance enhancement across the three channel widths (0.2D to 0.3D) reveals clear geometry–performance relationships. These findings provide valuable insights for optimizing fluidic oscillator designs in applications requiring high-frequency oscillations and targeted cooling, such as electronics or gas turbine blade cooling.