We investigate the growth of stellar discs in Milky Way-mass galaxies using the magnetohydrodynamical simulations of the Auriga Project in a full cosmological context. We focus on the gas accretion process along the discs, calculating the net, infall and outflow rates as a function of galactocentric distance, and investigate the relation between them and the star formation activity. The stellar distributions of around 70 per cent of the simulated galaxies exhibit an 'inside-out' pattern, with older (younger) stellar populations preferentially located in the inner (outer) disc regions. In all cases, we find a very tight correlation between the infall, outflow, and net accretion rates, as well as between these three quantities and the star formation rate. This is because the amount of gas which is ultimately available for star formation in each radial ring depends not only on the infall rates, but also on the amount of gas leaving the disc in outflows, which directly relates to the local star formation level. Therefore, any of these rates can be used to identify galaxies with inside-out growth. For these galaxies, the correlation between the dominant times of accretion/star formation and disc radius is well fitted by a linear function. We also find that, when averaged over galaxies with formation histories similar to the Milky Way, the simulated accretion rates show a similar evolution (both temporally and radially integrated) to the usual accretion prescriptions used in chemical evolution models, although some major differences arise at early times and in the inner disc regions.