The rise of flexible electronics calls for cost-effective and scalable batteries with good mechanical and electrochemical performance. In this work, we developed printable, polymer-based AgO-Zn batteries featuring flexibility, rechargeability, high areal capacity, and low impedance. Using elastomeric composites, the current collectors, electrodes, and separators can be fabricated via a high-throughput, scalable, and layer-by-layer screen-printing process and vacuum-sealed in a stacked configuration. The batteries are customizable in sizes and capacities, with the highest obtained areal capacity of 54 mAh/cm² for primary applications. Advanced X-ray tomography, impedance spectroscopy, and rigorous deformation tests were used to characterize the battery. The batteries were used to power a flexible E-ink display system that requires a high-current drain and exhibited superior performance compared to commercial lithium coin cells under the same pulsed-discharge conditions. The developed battery presents a practical solution for powering a wide range of electronics and holds major implications for the future development of high-performance flexible batteries.