The pressure-driven flow of a suspension of spinning particles in a rectangular channel is studied using an acoustic method. The suspension is made of insulating particles [poly(methyl methacrylate)] dispersed in a slightly conducting oil (Ugilec+Dielec) and is subjected to a direct current electric field. In such a case, the particles are polarized in the direction opposite to that of the electric field and begin to rotate in order to flip their dipoles in the field direction. Such a rotation of the particles is known as Quincke rotation and is responsible for an important decrease of the effective viscosity of the suspension. Indeed, due to the electric torque exerted on the particles, the stress tensor in the suspension is not symmetric anymore and a driving effect arises from the anti-symmetric part. When such a suspension flows through a rectangular channel, the velocity profile is expected to deviate from the usual Poiseuille flow. In this paper, the velocity profiles are measured using pulsed ultrasound Doppler velocimetry technique. They compare well to those that are computed from the otherwise measured rheological law.