Differential equations and boundary conditions for the flow velocity and the tensor polarization are solved for a cylindrical Couette-flow apparatus in a magnetic field. The ensuing Knudsen corrections for flow birefringence in gases consist of two contributions: (i) the velocity gradient is reduced by slip of the gas at the walls, (ii) the tensor polarization itself is influenced by gas-wall collisions. As a result, flow birefringence decreases for low pressures. For the gases HD, N2 and CO the relevant surface parameters are already known from Knudsen corrections for the Senftleben- Beenakker effect of viscosity. Thus the explicit pressure dependence of flow birefringence can be predicted for these gases (for zero magnetic field) and for the apparatus used by Baas