We present a numerical study of transport phenomena involving chemically reactive species, modeled by advection–diffusion–reaction systems coupled with flow governed by Darcy’s law. Spatial discretization of both velocity and concentrations is performed using the Virtual Element Method, while time discretization relies on a discontinuous Galerkin scheme. This work constitutes a preliminary investigation based on simplified modeling assumptions, including concentration-independent viscosity in the Darcy problem, constant diffusion tensors in the transport equations, and first-order reaction networks with liquid-phase degradation. We derive an abstract a priori error estimate using a technique that combines Gauss–Radau interpolation with numerical integration. Numerical results validate the theoretical analysis and exhibit arbitrary-order accuracy in space and time.