ABSTRACT Dusty, neutral outflows and inflows are a common feature of nearby star-forming galaxies. We characterize these flows in eight galaxies – mostly active galactic nuclei (AGN) – selected for their widespread Na i D signatures from the Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7). This survey employs deep, wide field-of-view (FOV) integral field spectroscopy at moderate spectral resolution (R = 7000 at Na i D). We significantly expand the sample of sightlines in external galaxies in which the spatially resolved relationship has been studied between cool, neutral gas properties – N(Na i), Weq(Na i D) – and dust – E(B − V) from both stars and gas. Our sample shows strong, significant correlations of total Weq with E(B − V)⋆ and g − i colour within individual galaxies; correlations with E(B − V)gas are present but weaker. Regressions yield slope variations from galaxy to galaxy and intrinsic scatter ∼1 Å. The sample occupies regions in the space of N(Na i) and $W_\mathrm{eq}^\mathrm{abs}$ versus E(B − V)gas that are consistent with extrapolations from other studies to higher colour excess [E(B − V)gas ∼ 1]. For perhaps the first time in external galaxies, we detect inverse P Cygni profiles in the Na i D line, presumably due to inflowing gas. Via Doppler-shifted Na i D absorption and emission lines, we find ubiquitous flows that differ from stellar rotation by $\gtrsim$100 km s−1 or have $|v_{\mathrm{ abs}} - v_{\mathrm{ em}}|\gtrsim 100$ km s−1. Inflows and outflows extend towards the edge of the detected stellar disc/FOV, together subtend 10–40 per cent of the projected disc, and have similar mean N(Na i) and Weq(Na i D). Outflows are consistent with minor axis or jet-driven flows, while inflows tend towards the projected major axis. The inflows may result from non-axisymmetric potentials, tidal motions, or halo infall.