Pastes containing reduced graphene oxide (rGO) and SnCl2 solution were screen printed on carbon cloth and then calcined using a CO2 tornado-type atmospheric-pressure plasma jet (APPJ). The tornado circulation of the plasma gas enhances the mixing of the reactive plasma species and thus ensures better reaction uniformity. Scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and X-ray photoelectron spectroscopy (XPS) were performed to characterize the synthesized rGO-SnO2 nanocomposites on carbon cloth. After CO2 tornado-type APPJ treatment, the pastes were converted into rGO-SnO2 nanocomposites for use as the active electrode materials of polyvinyl alcohol (PVA)-H2SO4 gel-electrolyte flexible supercapacitors (SCs). Various APPJ scanning times were tested to obtain SCs with optimized performance. With seven APPJ scans, the SC achieved the best areal capacitance of 37.17 mF/cm2 in Galvanostatic charging/discharging (GCD) and a capacitance retention rate of 84.2% after 10,000-cycle cyclic voltammetry (CV) tests. The capacitance contribution ratio, calculated as pseudocapacitance/electrical double layer capacitance (PC/EDLC), is ~50/50 as analyzed by the Trasatti method. GCD data were also analyzed to obtain Ragone plots; these indicated an energy density comparable to those of SCs processed using a fixed-point nitrogen APPJ in our previous study.