Developing new flexible and electroactive materials is a significant challenge to producing safe, reliable, and environmentally friendly energy storage devices. This study introduces a promising electrolyte system that fulfills these requirements. First, polypyrrole (PPy) nanotubes are electropolymerized in graphite-thread electrodes using methyl orange (MO) templates in an acidic medium. The modification increases the conductivity and does not compromise the flexibility of the electrodes. Next, flexible supercapacitors are built using hydrogel prepared from poly(vinyl alcohol) (PVA)/sodium alginate (SA) obtained by freeze–thawing and swollen with ionic solutions as an electrolyte. The material exhibits a homogenous and porous hydrogel matrix allowing a high conductivity of 3.6 mS cm−1 as-prepared while displaying great versatility, changing its electrochemical and mechanical properties depending on the swollen electrolyte. Therefore, it allows its combination with modified graphite-thread electrodes into a quasi-solid electrochemical energy storage device, achieving a specific capacitance (Cs) value of 66 F g−1 at 0.5 A g−1. Finally, the flexible device exhibits specific energy and power values of 19.9 W kg−1 and 3.0 Wh kg−1, relying on the liquid phase in the hydrogel matrix produced from biodegradable polymers. This study shows an environment friendly, flexible, and tunable quasi-solid electrolyte, depending on a simple swell experiment to shape its properties according to its application.