Magnetohydrodynamic MHD flow of a RedOx electrolyte in a straight conduit is investigated theoretically. Inert electrodes are deposited along segments of the opposing walls of a straight conduit that is filled with a RedOx electrolyte solution. The conduit is positioned in a uniform magnetic field. When a potential difference is applied across the opposing electrodes, the resulting current interacts with the magnetic field to induce Lorentz forces. The species' mass transport and the momentum equation are coupled and must be solved simultaneously. We compute the various species' concentration distributions, the current flux distribution, and the liquid's motion in the absence and presence of pressure gradients. The pressure gradients may either assist or oppose the MHD flow. At low potential differences, the current and the induced MHD flow increase nearly linearly as the potential difference increases. When the potential difference exceeds a certain critical value, the current and the flow rate saturate. We demonstrate that it is advantageous to use multiple electrode pairs with dielectric gaps between adjacent electrodes rather than a single electrode pair with an equivalent length. Finally, MHD flow with RedOx solution in the presence of abundant supporting electrolyte under limiting current conditions is analyzed using boundary layer theory. The approximate analytical solutions for the ions concentrations and the current agree well with the numerical solutions.