  We perform a stacking analysis of the neutral
\nad\,$\lambda\lambda$5889,5895\,\AA\ ISM doublet using the SDSS DR7
spectroscopic data set to probe the prevalence and characteristics of cold
(T\,$\lesssim$\,10$^{4}$\,K) galactic-scale gas flows in local (0.025$\leqslant
z\leqslant$0.1) inactive and AGN-host galaxies across the SFR-M$_{*}$ plane. We
find low-velocity outflows to be prevalent in regions of high SFRs and stellar
masses (10 $\lesssim$log M$_{*}$/M$_{\odot}$ $\lesssim$ 11.5), however we do
not find any detections in the low mass (log M$_{*}$/M$_{\odot}$ $\lesssim$ 10)
regime. We also find tentative detections of inflowing gas in high mass
galaxies across the star-forming population. We derive mass outflow rates in
the range of 0.14-1.74\,M$_{\odot}$yr$^{-1}$ and upper limits on inflow rates
<1\,M$_{\odot}$yr$^{-1}$, allowing us to place constraints on the mass loading
factor ($\eta$=$\dot{M}_{\text{out}}$/SFR) for use in simulations of the local
Universe. We discuss the fate of the outflows by comparing the force provided
by the starburst to the critical force needed to push the outflow outward, and
find the vast majority of the outflows unlikely to escape the host system.
Finally, as outflow detection rates and central velocities do not vary strongly
with the presence of a (weak) active supermassive black hole, we determine that
star formation appears to be the primary driver of outflows at $z\sim$0.
