We measure Redshift-Space Distortions (RSD) in the two-point correlation function of a sample of 63,163 spectroscopically identified galaxies with z<0.2, an epoch where there are currently only limited measurements, from the Sloan Digital Sky Survey (SDSS) Data Release 7 Main Galaxy Sample. Our sample, which we denote MGS, covers 6,813 deg2 with an effective redshift zeff=0.15 and is described in our companion paper (Paper I), which concentrates on BAO measurements. In order to validate the fitting methods used in both papers, and derive errors, we create and analyse 1000 mock catalogues using a new algorithm called PICOLA to generate accurate dark matter fields. Haloes are then selected using a friends-of-friends algorithm, and populated with galaxies using a Halo-Occupation Distribution fitted to the data. Using errors derived from these mocks, we fit a model to the monopole and quadrupole moments of the MGS correlation function. If we assume no Alcock-Paczynski (AP) effect (valid at z=0.15 for any smooth model of the expansion history), we measure the amplitude of the velocity field, fσ8, at z=0.15 to be 0.49+0.15−0.14. We also measure fσ8 including the AP effect. This latter measurement can be freely combined with recent Cosmic Microwave Background results to constrain the growth index of fluctuations, γ. Assuming a background ΛCDM cosmology and combining with current Baryon Acoustic Oscillation data we find γ=0.64±0.09, which is consistent with the prediction of General Relativity (γ≈0.55), though with a slight preference for higher γ and hence models with weaker gravitational interactions.