Buoyancy-driven hydrodynamic instabilities of a miscible reactive interface in a homogeneous porous medium is examined. A bimolecular chemical reaction (A+B→C) is triggered at the interface between two reactant solutions A and B resulting in a chemical product solution C with different density and the viscosity from those of the reactants. The effects of the chemical reaction and a transverse flow parallel to the initial interface between the reactants are numerically analyzed. It was found that as a result of the transverse flow, fingers with sharp concentration gradients tend to develop and advance fast downward leading to higher rates of chemical production. Furthermore, a detailed analysis of the finger growth and the effects of buoyancy, transverse flow and chemical reaction allowed to reach a physical interpretation of the trends observed. Finally, a special tuning of the transverse velocity is proposed to ensure maximum or minimum chemical production applicable to subsurface flows.