Small angle neutron scattering (SANS) has been utilized to investigate the flow properties of the discotic micellar isotropic (I), nematic (N) and lamellar (L-alpha) phases in aqueous solutions of cesium perfluoro-octanate. Under simple shear, no preferred orientation was observed in the I phase. The N phase aligned with the nematic director along the shear gradient velocity, providing the first evidence for a positive value of the viscosity parameter, alpha(2). The L-alpha phase oriented with lamellae parallel to the shear plane. A reorientation of the director near the N-L-alpha transition was witnessed upon cooling from the N phase at a constant shear rate and is attributed, primarily to a change in the value of alpha(2) as a result of increasing lamellar correlations in the nematic phase. The application of oscillatory shear induced significant shifts in the phase boundaries, including nematic-like order some 7 K into the quiescent I phase.