Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending and it is used by the Outer Hair Cells (OHC) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHC is to find the relations and impact of the electro-mechanical properties of the membrane, the rheological properties of the viscoelastic Burgers’s media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, which are characterized by the Jeffreys constitutive equation with different material conditions. The membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. Assuming small Deborah number, the average membrane curvature or volumetric rate flow as a function of the electrical field can be expressed as a third order differential equation which depend on the material properties in the system. Neglecting the inertial mechanisms, the system can be expressed in terms of a spring and dashpots such as a mechanical system. Taking into account the inertial mechanisms, the power spectrum shows several resonance peaks in the average membrane curvature and volumetric flow rate. When the inertia is neglected, the system shows a non-monotonically behavior in the power spectrum.