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Abridged. The bright-rimmed cloud IC1396N hosts CO, H$_2$, and Herbig-Haro outflows powered by millimetre compact sources. We aim to characterise the kinematics and physical conditions of the H$_2$ emission features spread over IC1396N, which appear as chains of knots with a jet-like morphology, tracing different H$_2$ outflows, and to obtain further information about (and an identification of) the driving sources. Low-resolution, long-slit near-infrared spectra were acquired with NICS at the TNG, using grisms KB (R~1200), HK and JH (R~500). Several slit pointings and PA were used throughout IC1396N to sample a number of the H$_2$ knots previously detected in deep H$_2$ 2.12 $μ$m 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 IC1396N H$_2$ outflows were derived. These also allowed estimating extinction ranges towards several features. [FeII] emission was only detected towards a few knots, which also display unusually large 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) appears as a set of features trailing a leading bow-shock structure consistent with the results of 3-D magneto-hydrodynamical models. Either side of the leading bow-shock (A15) exhibits a different radial velocity, whose possible explanations are discussed in the paper. Our data cannot confirm whether strands A and B have both been originated by the intermediate mass young stellar object BIMA 2.