Embryo morphogenesis involves a complex combination of pattern-forming mechanisms. However, classical in vitro patterning experiments explore only one mechanism at a time, thus missing coupling effects. Here, we conjugate two major pattern-forming mechanisms —reaction-diffusion and active matter— by integrating dissipative DNA/enzyme reaction networks within an active gel composed of cytoskeletal motors and filaments. We show that the strength of the flow generated by the active gel controls the mechano-chemical coupling between the two subsystems. We use this property to engineer the mechanical activation of chemical reaction networks both in time and space, thus mimicking key aspects of the polarization mechanism observed in C. elegans oocytes. We anticipate that reaction-diffusion active matter may be useful to investigate mechano-chemical transduction and to design new materials with life-like properties.