Proton chemistry is becoming a focal point in the development of zinc‐ion energy storage devices due to its swift H+ insertion/extraction kinetics. This characteristic feature confers to electrodes a remarkable power density, rate capability, and prolonged cycling durability. However, the storage mechanism of H+ in electrodes based on covalent‐organic frameworks (COFs) has not been thoroughly investigated. In this work, we introduce an unprecedented concept involving a supramolecular approach based on the design of a benzotrithiophene‐sulfonate COF (COF‐BTT‐SO3H) with remarkable storage capacity for simultaneous insertion and extraction of H+ and Zn2+. The ad hoc positioning of the ‐SO3H groups within the COF‐BTT‐SO3H structure facilitates the formation of a robust H‐bonded network. Through density functional theory calculations and employing in situ and ex situ analyses, we demonstrate that this network functions as a spontaneous proton ion pump leading to enhanced ion‐diffusion kinetics and exceptional rate performance in zinc‐ion energy storage devices. COF‐BTT‐SO3H reveals a high capacity of 294.7 mAh/g (0.1 A/g), a remarkable maximum energy density of 182.5 Wh/kg, and power density of 14.8 kW/kg, which are superior to most of the reported COF‐based electrodes or other organic and inorganic electrode materials in Zn2+ energy storage devices.