Fluid and charge transport in micro- and nanoscale fluidic systems are intrinsically coupled via electrokinetic phenomena. While electroosmotic flows and streaming potentials are well understood for externally imposed stimuli, charge injection at electrodes localized inside fluidic systems via electrochemical processes remains to a large degree unexplored. Here, we employ ultramicroelectrodes and nanogap electrodes to study the subtle interplay between ohmic drops, streaming currents, and faradaic processes in miniaturized channels at low concentrations of supporting electrolyte. We show that electroosmosis can, under favorable circumstances, counteract the effect of ohmic losses and shift the apparent formal potential of redox reactions. This interplay can be described by simple circuit models, such that the results described here can be adapted to other micro- and nanofluidic electrochemical systems.