Flexible solid state supercapacitors have gained significant importance in energy storage device technology. In this work, flexible solid-state supercapacitors are designed with enhanced capacitance, bending cycle stability and energy density. Activated carbon (AC) is synthesized from cabbage leaves and boron doped reduced graphene oxide (BRGO) is incorporated into AC to improve mechanical flexibility. On the other hand, carbon quantum dots (CQDs) and acetonitrile (ACN) as solvent are incorporated into a gel electrolyte. We investigate the concentration of boron in the electrode material and that of CQDs in the gel electrolyte and reveal that the capacitance, bending properties and energy density of the solid-state supercapacitor are simultaneously improved with the optimum composition of AC/BRGO in the CQD/gel electrolyte. This demonstration of composite electrode and electrolyte materials could substantially improve the capacitance, cycle stability and energy density of solid-state supercapacitors.