The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.