Redox-active small molecules, used traditionally in redox flow batteries (RFBs), are susceptible to crossover and require expensive ion exchange membranes (IEMs) to achieve long lifetimes. Redox-active polymer (RAP) solutions show promise as candidate electrolytes to mitigate crossover through size exclusion, enabling the use of porous separators instead of IEMs. For oxidized RAPs, ionic conductivity varies weakly between 1.6 and 2.1 S/m for RAP concentrations of 0.13-1.27 mol/kg (monomeric repeat unit per kg solvent) and 0.32 mol/kg LiBF4 with a minor increase upon reduction. In contrast, viscosity varies between 1.8 and 184.0 mPa-s over the same concentration range with weakly shear-thinning rheology independent of oxidation state. Subsequently, we use porous-electrode modeling to predict the cycling dynamics of RFBs using RAPs. We find that achievable power densities are limited by ohmic transport in the electrolyte when suitably large flow rates are used to overcome capacity losses due to mixing within tanks.