We present new measurements of the coherent motion of galaxies based on observations of the large-scale redshift-space distortions seen in the two-dimensional two-point correlation function of Luminous Red Galaxies in Data Release Seven of the Sloan Digital Sky Survey. We have developed a new methodology for estimating these coherent motions, which is less dependent on the details of galaxy bias and of the cosmological model to explain the late-time acceleration of the expansion of the Universe. We measure a one-dimensional velocity dispersion of galaxies on large-scales of σv = h-1 Mpc and σv = h-1 Mpc at a mean redshift of z = 0.25 and 0.38 respectively. These values are fully consistent with predictions for a WMAP7-normalised ΛCDM Universe and inconsistent at confidence of 3.8σ with a Dvali-Gabadadze-Porrati (DGP) model for the Universe. We can convert the units of these σv measurements to km/s and km/s respectively (assuming a ΛCDM universe), which are lower that expected based on recent low redshift (z < 0.2) measurements of the peculiar velocity field (or "bulk flows"). It is difficult to directly compare these measurements as they cover different redshift ranges and different areas of the sky. However, one possible cosmological explanation for this discrepancy is that our Galaxy is located in unusually over, or under, dense region of the Universe.