NGC 2915 is a nearby blue compact dwarf with a differentially rotating H i disc extending out to ∼5 R-band R25 radii. This disc serves as an ideal tracer of the system's gravitational potential in regions of the galaxy that are dominated by dark matter. We use new H i synthesis observations of NGC 2915, obtained with the Australia Telescope Compact Array, to search for non-circular flows within the outer H i disc. Two independent methods are used, and the results of each interpreted in the context of relevant axisymmetric and non-axisymmetric perturbations of the potential. We find evidence for: (i) elliptical streaming associated with the spiral structure of the H i disc and the central bar-like feature in the mass distribution; (ii) a spherical dark matter halo; and (iii) an axisymmetric radial outflow of ∼5–17 km s−1 (∼6–20 per cent of the circular speed). A possible bar-like perturbation of the potential hinders attempts to unambiguously detect kinematic signatures of radial flows in the H i velocity field. The radial outflows are inconsistent with the possible disc formation scenario in which gas from the surrounding intergalactic medium is deposited on the outer H i disc and then transported towards the centre of the galaxy. They are, however, consistent with the possibility of some material being redistributed towards the outer disc in order to conserve angular momentum as material flows inwards along a bar.