We investigate the unstable flow of wormlike micelle solutions in pressure driven capillary flow, with a focus on the effect of entrance geometry on the fluid fluctuations. The flow is measured at different points in the capillary using particle image velocimetry while simultaneously measuring the pressure drop across the entire capillary. The fluctuations are characterized by rapid flow rate jumps that correspond with a decrease in the pressure drop followed by a longer recovery period. Velocimetry measurements in the entrance region show a transition to unstable flow above a critical flow rate, where large flow circulations are observed in the tapered geometry and localized jets are observed in an abrupt contraction. The transition to this unstable flow is shown to occur at a similar dimensionless extension rate normalized by the micelle relaxation time. A rapid breakdown in micelle alignment is observed in polarized light microscopy at the onset of the flow rate jump, indicating the importance of rapid micelle structural changes on the fluctuations. We characterize the system by analyzing the power spectral densities and develop a dynamical systems model to describe the relationship between pressure and flow rate. These developments provide understanding to control flow fluctuations and motivation for more detailed study of the coupling of fluid microstructure transitions and flow fluctuations.