Membrane flexoelectricity is an electromechanical coupling effect between the membrane average curvature and macroscopic electric polarization, which is essential to the physiology of hearing. Flexoelectric actuation uses an imposed electric field to create membrane bending and is used by the Outer Hair Cells (OHCs) located in the inner ear. Motivated by the functioning of the OHC, in this paper we model the small amplitude oscillatory dynamics of a tethered circular membrane immersed in Burgers viscoelastic media driven by a small amplitude harmonic electric field of arbitrary frequency. The model for membrane average curvature dynamics as a function of the electric field dynamics is second order in both inputs and outputs and maps into the classical mechanical Burgers solid model. The three dimensional material space that characterizes the inertia, viscosity, and elasticity of the viscoelastic fluid/flexoelectric membrane material system is defined and used to classify and characterize the frequency response of the electro-mechanical system. The frequency response is characteristic of a second order dynamical system with a second order input and can display a single resonant peak in the total power. The amplitude, frequency and width of the power peak, of relevance to the functioning of OHC is dependent on the inertia emerging from the contacting viscoelastic phases and the ratio between the membrane elasticity and the elasticity of contacting liquids. The integrated flexoelectric/viscoelastic model and the novel findings contribute to the ongoing quest for a fundamental understanding of the functioning of outer hair cells (OHCs)