We present a measurement of the velocity flow of the local universe relative to the CMB rest frame, based on the Jha, Riess & Kirshner (2007) sample of 133 low redshift type Ia supernovae. At a depth of 4500 km/s we find a dipole amplitude of 279+-68 km/s in the direction (l,b) = (285+-18,-10+-15), consistent with earlier measurements and with the assumption that the local velocity field is dominated by the Great Attractor region. At a larger depth of 5900 km/s we find a shift in the dipole direction towards the Shapley concentration. We also present the first measurement of the quadrupole term in the local velocity flow at these depths. Finally, we have performed detailed studies based on N-body simulations of the expected precision with which the lowest multipoles in the velocity field can be measured out to redshifts of order 0.1. Our mock catalogues are in good agreement with current observations, and demonstrate that our results are robust with respect to assumptions about the influence of local environment on the type Ia supernova rate.