This paper examines the effects of flow on the collapse behavior of grafted polyelectrolyte layers in uniform permeation flows of poor solvent within a model based on the Alexander-deGennes ansatz that all chains behave alike in flow. This model accounts for both the polymer-solvent drag forces and the possible effects of solvent drag forces on the counterions within in the brush. The phase behavior of charged brushes under now is examined in the limits of low and moderate charge per unit grafting area. In both limits, it is found that the first-order nature of the stretch-collapse transition occurring for Alexander-deGennes polyelectrolyte brushes in quiescent poor solvents also remains in the presence of solvent flow. However, there is a significant shift in the location of the first-order transition line and the second-order critical point as a function of solvent flow rate. In particular, the flow generally shifts the critical point and transition line toward smaller polyelectrolyte charge for flows out of the brush and toward larger polyelectrolyte charge for flows into the brush. As well as modifying the location of the transition, solvent flow also changes the susceptibility of the brush : the discontinuity in brush thickness across the transition line is a rapidly increasing function of solvent flow rate. Possible modifications due to structural inhomogeneities are briefly discussed.