We explore the mechanisms of voltage-induced textural switching and the corresponding electro-optical responses of a binary cholesteric liquid crystal (CLC) composed of the rod-like nematic LC E7 with positive dielectric anisotropy and the bent-core LC dimer CB7CB with large flexoelectric coefficients. Our results indicate that the minimal voltage (V H) required for retaining the CLC in the homeotropic state and the optical transparency of the CLC after treating with decreasing voltage (from V H to zero) are dependent on the voltage frequency. The observed frequency modulated electro-optical properties are characterized by the frequency regimes separated by the critical frequencies of flexoelectric polarization and dielectric relaxation in dielectric dispersion. These unusual features, specific to the CB7CB-doped CLC, are explained by the dielectric and frequency-dependent flexoelectric responses of LC molecules to an external AC voltage. Accordingly, in addition to the known Grandjean planar and focal conic states, the uniform lying helix as a third stable state can be feasibly generated in the binary CLC with 45 wt% CB7CB by two pathways. The first one is to treat the cell directly with a sufficient voltage lower than V H; the other is to decrease the voltage gradually from V H to zero in the low-frequency regime, where the flexoelectric strength is significant. Manifested by its optical tristability, frequency-controllable optical transparency, and fast flexoelectro-optical response, the proposed binary rod-like/bent-core CLC system is promising for developing a variety of memory- and dynamic-mode photonic and optoelectronic devices.