We present a detailed analysis of the neutral hydrogen kinematics of 12 nearby dwarf irregular galaxies observed as part of the Local Volume H i Survey conducted at the Australia Telescope Compact Array. For each galaxy we measure the disc parameters (inclination, position angle) and the H i rotation curve. Six galaxies in our sample (AM 0605−341, Argo Dwarf, ESO 059−G001, ESO 137−G018, ESO 174−G?001 and ESO 308−G022) have their atomic hydrogen distribution studied for the first time. AM 0605−341 was found to have an extension of redshifted H i which we propose is due to a tidal interaction with NGC 2188. There is evidence that ESO 215−G?009 has extraplanar H i gas. We also compare the global galaxy properties, in particular the integrated H i flux density and velocity widths of the observed H i spectra, with the results from the low angular resolution H i Parkes All Sky Survey. We discuss under what circumstances the 21 cm emission-line profile can accurately predict the galaxies rotation velocity, an observational parameter crucial to study the classical and baryonic Tully–Fisher relations.