The bright-rimmed cloud IC 1396N, associated with an intermediate-mass star-forming region, hosts a number of CO, molecular hydrogen, and Herbig-Haro (HHs) outflows powered by a set of millimetre compact sources. The aim of this work is to characterise the kinematics and physical conditions of the H_2_ emission features spread throughout the IC 1396N region. The features appear as chains of knots with a jet-like morphology and trace different H_2_ outflows. We also obtain further information about (and an identification of) the driving sources. Low-resolution, long-slit near-infrared spectra were acquired with the NICS camera at the TNG telescope, using grisms KB (R~1200), HK, and JH (R~500). Several slit pointings and position angles were used throughout the IC 1396N region in order to sample a number of the H_2_ knots that were previously detected in deep H_2_ 2.12um images. The knots exhibit rich ro-vibrational spectra of H_2_, consistent with shock-excited excitation, from which radial velocities and relevant physical conditions of the IC 1396N H_2_ outflows were derived. These also allowed estimating extinction ranges towards several features. [FeII] emission was only detected towards a few knots that also display unusually high H_2_ 1-0 S(3)/S(1) flux ratios. The obtained radial velocities confirm that most of the outflows are close to the plane of the sky. Nearby knots in the same chain often display different radial velocities, both blue-shifted and red-shifted, which we interpret as due to ubiquitous jet precession in the driving sources or the development of oblique shocks. One of the chains (strand A, i.e. knots A1 to A15) appears as a set of features trailing a leading bow-shock structure consistent with the results of 3D magneto-hydrodynamical models. The sides of the leading bow shock (A15) exhibit different radial velocities. We discuss possible explanations. Our data cannot confirm whether strands A and B have both originated in the intermediate mass young stellar object [BGE2002] BIMA 2 because a simple model of a precessing jet cannot account for their locations. Near-infrared spectroscopy has confirmed that most of the H_2_ ro-vibrational emission in IC 1396N is shock-excited rather than uv-excited in photon-dominated regions. It has shown a complex kinematical structure in most strands of emitting knots as well.