Dense suspensions of non-Brownian particles may partially behave as thixotropic yield stress fluids. We study the flow of such fluids between two concentric cylinders using a phenomenological structural kinetics model. The structural kinetics approach balances the simplicity of phenomenological continuum approaches with a simplified model for structure against the complexity a more fundamental model based on particle micromechanics. A modified version of Houska's model, which includes a diffusive term for the structural parameter, is considered. Depending on the breakdown rate of the structural parameter, shear-banding may be observed. For shear-banding in steady flows, the stress selection depends on the diffusion of the structural parameter. If there is no structural diffusion, the displacement of the interface between the flowing and the static regions fixes the stress at the interface during the transient flow. In the cases of very small diffusive coefficients, the stress at the fluid / solid interface converges to a limit value which is different from the yield stress of the structured material as expected without any diffusion. Nevertheless, the inner torque and the flow profile are quite similar in both cases and the differences are localized near the fluid / solid interface. For shear-banding, the gradients of the structural parameter and the strain rate are very abrupt but the continuity is preserved by the diffusion.