Binder free flexible symmetric supercapacitors are developed with nickel cobaltite micro-flowers coated poly(3,4-ethylenedioxypyrrole) (NiCo2O4@PEDOP) hybrid electrodes. Free standing films of carbon nano-fibers (CNF), synthesized by electrospinning, were sandwiched between the NiCo2O4@PEDOP hybrid and the electrolyte coated separators on both sides of the cells. The CNF film conducts both ions and electrons, and confines the charge at the respective electrodes, to result in an improved specific capacitance (SC) and energy density compared to the analogous cell without the CNF interlayers. High SC of 1,775 F g-1 at a low current density of 0.96 A g-1 and a SC of 634 F g-1 achieved at a high current density of 38 A g-1 coupled with a SC retention of ~95% after 5,000 charge-discharge cycles in the NCO@PEDOP/CNF based symmetric supercapacitor, are performance attributes superior to that achieved with NCO and NCO/CNF based symmetric cells. The PEDOP coating serves as a highly conductive matrix for the NCO micro-flowers and also undergoes doping/de-doping during charge-discharge, thus amplifying the overall supercapacitor response, compared to the individual components. The CNF interlayers show reasonably high ion-diffusion coefficients for K+ and OH- propagation implying facile pathways available for movement of ions across the cross-section of the cell, and they also serve as ion reservoirs. The electrode morphologies remain unaffected by cycling, in the presence of the CNF interlayer. LED illumination and a largely unaltered charge storage response was achieved in a mutli-cell configuration, proving the potential for this approach in practical applications.