A dynamic model of a single-degree-of-freedom vibro-impact system with clearance under single-phase fluid flow is considered. The governing differential equations are solved numerically, and the multistable dynamics of the system are revealed through bifurcation diagrams, phase trajectories, and basins of attraction using the cell mapping method. Multiple flow velocity ranges are identified in which multiple vibrational motions coexist. A linear gain control strategy is employed by introducing a linear feedback coupling control signal composed of an attenuation function. The study focuses on switching between coexisting attractors without altering the system's primary parameters, thereby optimizing the response of the impact oscillator and avoiding chaotic responses induced by grazing bifurcations. This enables switching between different steady states, thereby enhancing the stability of such flow-induced vibration systems.