The rheological behavior of Brownian electrorheological (ER) fluids is studied as a model for flocculated colloidal dispersions. The ER fluid has the advantages that the interparticle potential energy can be varied by simply changing the applied field strength, and the microstructure consists of essentially linear chains of particles aligned with the field direction. Under simple shear flow, the suspension has a high-shear-rate Newtonian viscosity and a shear thinning viscosity at lower shear rates. For moderate attractive potential well depths, U-min/kT, the suspension has a low-shear viscosity that scales as exp(U-min/kT). Furthermore, the low-shear limiting behavior is seen at shear rates that scale as exp(-U-min/kT). A theory is proposed that makes use of the time scale of diffusion for aggregated particles out of their mutual potential well, tau similar to (a(2)/D)(kT/U-min)exp(U-min/kT), much in the spirit of the Eyring theory. Here a is the particle radius and D is the diffusivity of an isolated particle. When the shear rate is nondimensionalized by tau, the reduced viscosity data for all field strengths collapse onto a single universal curve. Although we use a relatively small monolayer suspension, our simulation results compare well to the limited experimental and theoretical work on Brownian ER suspensions. The scaling relationship for the low-shear viscosity has also been evidenced in other studies of flocculated dispersions.