We use simulations to probe the flow properties of dense two-dimensional magnetorheological fluids. Prior results from both experiments and simulations report that the shear stress σ scales with strain rate as σ ∼ 1-Δ, with values of the exponent ranging between 2/3 < Δ ≤ 1. However it remains unclear what properties of the system select the value of Δ, and in particular under what conditions the system displays a yield stress (Δ = 1). To address these questions, we perform simulations of a minimalistic model system in which particles interact via long ranged magnetic dipole forces, finite ranged elastic repulsion, and viscous damping. We find a surprising dependence of the apparent exponent Δ on the form of the viscous force law. For experimentally relevant values of the volume fraction φ and the dimensionless Mason number Mn (which quantifies the competition between viscous and magnetic stresses), models using a Stokes-like drag force show Δ ≈ 0.75 and no apparent yield stress. When dissipation occurs at the contact, however, a clear yield stress plateau is evident in the steady state flow curves. In either case, increasing φ towards the jamming transition suffices to induce a yield stress. We relate these qualitatively distinct flow curves to clustering mechanisms at the particle scale. For Stokes-like drag, the system builds up anisotropic, chain-like clusters as Mn tends to zero (vanishing strain rate and/or high field strength). For contact damping, by contrast, there is a second clustering mechanism due to inelastic collisions.