Dwarf irregular galaxies (dIrrs) are the smallest stellar systems with extended H i discs. The study of the kinematics of such discs is a powerful tool to estimate the total matter distribution at these very small scales. In this work, we study the H i kinematics of 17 galaxies extracted from the 'Local Irregulars That Trace Luminosity Extremes, The H i Nearby Galaxy Survey' (LITTLE THINGS). Our approach differs significantly from previous studies in that we directly fit 3D models (two spatial dimensions plus one spectral dimension) using the software 3Dbarolo, fully exploiting the information in the H i data cubes. For each galaxy, we derive the geometric parameters of the H i disc (inclination and position angle), the radial distribution of the surface density, the velocity-dispersion (σv) profile and the rotation curve. The circular velocity (Vc), which traces directly the galactic potential, is then obtained by correcting the rotation curve for the asymmetric drift. As an initial application, we show that these dIrrs lie on a baryonic Tully-Fisher relation in excellent agreement with that seen on larger scales. The final products of this work are high-quality, ready-to-use kinematic data (Vc and σv) that we make publicly available. These can be used to perform dynamical studies and improve our understanding of these low-mass galaxies.