A portable paper‐based organic redox flow primary battery using sustainable quinone chemistry is presented. The compact prototype relies on the capillary forces of the paper matrix to develop a quasi‐steady flow of the reactants through a pair of porous carbon electrodes without the need of external pumps. Co‐laminar capillary flow allows operation Under mixed‐media conditions, in which an alkaline anolyte and an acidic catholyte are employed. This feature enables higher electrochemical cell voltages during discharge operation and the utilization of a wider range of available species and electrolytes and provides the advantage to form a neutral or near‐neutral pH as the electrolytes neutralize at the absorbent pad, which allows a safe disposal after use. The effects of the device design parameters have been studied to enhance battery features such as power output, operational time, and fuel utilization. The device achieves a faradaic efficiency of up to 98 %, which is the highest reported in a capillary‐based electrochemical power source, as well as a cell capacity of up to 11.4 Ah L−1 cm−2, comparable to state‐of‐the‐art large‐scale redox flow cells.