Origami wrapping fold patterns, also known as flashers, allow for the n-fold rotationally symmetric wrapping of a sheet around a central polygon. We show how origami flashers may tessellate the plane through regular and semi-regular tilings. Crucially, both the folded and unfolded forms can be shown to tessellate. This allows for the entire tessellation to fold regardless of the number of unit cells. This work has the potential to impact the design of modular shape-changing structures. We present conditions on zero-thickness flasher unit cells that allow for tessellation via regular and semi-regular tilings. Each such tessellation corresponds to a family of flasher-based fold patterns. Additionally, we present an algorithm to generate thickness-accommodating spiral-wrapped flasher unit cells that can tessellate.