Printed textile-based flexible batteries are gaining attention in several applications, but they are becoming more relevant to the health care industry in terms of realizing wearable and skin-conformable electronic devices. A flexible battery must ideally be deformable along multiple directions. In this work, with an aim to develop a fully printed omnidirectional deformable battery, we report the fabrication process of a novel single-polymer-based flexible non-rechargeable planar Ag2O-Zn battery on a textile substrate using the stencil printing method. Except for the electrolyte, all the components of the battery, including the current collectors, the anode, the cathode, and the separator membrane, are fabricated using a single polymer, namely styrene–ethylene–butylene–styrene (SEBS). To fabricate the SEBS separator, we introduce the solvent evaporation-induced phase separation (SEIPS) process. In the SEIPS method, toluene and dimethyl sulfoxide (DMSO) are selected as the solvent–nonsolvent pair. The SEBS: toluene: DMSO system with a wt% ratio of 6:85:9 showed improved performance regarding the OCV tests. A polyacrylic acid (PAA)-based alkaline polymer gel is used as an electrolyte. The demonstrated process is simple, and, with suitable modifications, it should find its use in the development of digitally printed alkaline batteries.