Dense suspensions can exhibit a dramatic stress-induced transition from liquid-like to solid-like behavior. In many materials, the solid-like flow state is characterized by large flow fluctuations and instabilities. Although various experiments have been performed to characterize flow fluctuations, the mechanisms that govern the flow instabilities remain poorly understood. To elucidate these mechanisms, we characterize a system that rapidly fluctuates between two flow states. One of the flow states is dominated by apparent wall slip, and the other is dominated by dilatancy. The dilatant regimeoccurs at elevated stresses and is associated with reduced wall slip, whereas the wall slip-dominated regime occurs at lower stresses. At stresses that are intermediate between these two regimes, the material fluctuates between the two regimes in a semi-regular fashion. Our analysis of the fluctuations at millisecond timescales shows that fluctuations occur because neither regime is capable of supporting a constant stress in a stable manner. We rationalize our results in terms of the differences in the shear-induced particle pressure between regions that are particle-rich and regions of slip that are particle-depleted.