Recently, the development of bio-inspired aircrafts has broad application prospects. However, the flow separation in the boundary layer of the bio-inspired wing under low Reynolds number becomes a great challenge for the design of a novel bio-inspired aircraft. It is worth noting that birds in nature can easily control flow separation, thanks to the flap-like flexible plumes attached to their wing surfaces. In this paper, the unsteady flow control of the flexible flap is studied by the immersed boundary-lattice Boltzmann-finite element method (IB-LB-FEM). The mechanism of flow separation on the airfoil surface at a bio-inspired large angle of attack (AOA) is suggested. The effects of the flexible flap position and its material properties on the unsteady flow control of the airfoil at large AOA are systematically discussed. The deformation law of the flexible flap with fluid–structure interaction (FSI) is revealed, and its influence on unsteady aerodynamics of the airfoil is discussed. The results show that with the increase in the AOA, the aerodynamic characteristics of the airfoil change with time from “periodic state” to “chaotic state” to “quasi-periodic state,” which is closely related to the unsteady flow separation on the airfoil upper surface. The new induced vortex is formed at the end of the flexible flap because of the FSI, which enhances or weakens the strength of vortices on the airfoil surface, affecting the aerodynamics of the airfoil. The flow control mechanism of the flexible flap proposed in this paper will provide a new design idea for the novel bio-inspired aircraft.