  We explore the possibility that matter bulk flows could generate the required
vorticity in the electron-proton-photon plasma to source cosmic magnetic fields
through the Harrison mechanism. We analyze the coupled set of perturbed Maxwell
and Boltzmann equations for a plasma in which the matter and radiation
components exhibit relative bulk motions at the background level. We find that,
to first order in cosmological perturbations, bulk flows with velocities
compatible with current Planck limits ($\beta<8.5\times 10^{-4}$ at $95\%$ CL)
could generate magnetic fields with an amplitude $10^{-21}$ G on 10 kpc
comoving scales at the time of completed galaxy formation which could be
sufficient to seed a galactic dynamo mechanism.
