Polyvinyl alcohol (PVA) based gel/solid-state electrolytes are commonly used in the fabrication of the flexible supercapacitor (FSC) due to its bio-degradable nature, economic, non-toxic, hydrophilicity, high dielectric constant, and mechanical strength. Though, the less ionic conductivity of gel electrolyte (GE) limits the specific capacitance, energy density, rate performance and cycle life of the FSC. Moreover, the high self-discharge rate due to the internal resistance of FSC is also affecting the electrochemical performance. Here, we introduce the facile and innovative approach to snowball the ionic conductivity of the GE (here, PVA/H2SO4) as well as reduce the self-discharge of FSC by the addition of poly (3,4- ethylenedioxythiophene) polystyrene sulfonate (PEDOT-PSS), and B, S co-doped graphene (BSGO) deployed as an electrode material for the fabrication of FSC. The addition of PEDOT-PSS in PVA/H2SO4 improved the ionic conductivity (from 2.6 to 14 mS/cm), energy density (from 4 to 10 Wh/kg), and rate capability (from 50% to 80%) of FSC appreciably. Besides, high self-discharge of FSC is largely mitigated. At most, 72% of working voltage has been retained after 2400 s for FSC in an open circuit mode. The considerable change in the ionic conductivity, energy density and self-discharge after the addition of PEDOT-PSS with PVA/H2SO4 might be due to the reversible redox reactions of sulfonate ions in PEDTO-PSS with H+ ions.