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Results. We illustrate our profile-fitting technique and present the K\,{\sc i} velocity structure of the dense ISM along the paths to all targets. As a validation test of the dust map, we show comparisons between distances to several reconstructed clouds with recent distance assignments based on different techniques. Target star extinctions estimated by integration in the 3D map are compared with their K\,{\sc i} 7699 A absorptions and the degree of correlation is found comparable to the one between the same K\,{\sc i} line and the total hydrogen column for stars distributed over the sky that are part of a published high resolution survey. We show images of the updated dust distribution in a series of vertical planes in the Galactic longitude interval 150-182.5 deg and our estimated assignments of radial velocities to the opaque regions. Most clearly defined K\,{\sc i} absorptions may be assigned to a dense dust cloud between the Sun and the target star. It appeared relatively straightforward to find a velocity pattern consistent will all absorptions and ensuring coherence between adjacent lines of sight, at the exception of a few weak lines. We compare our results with recent determinations of velocities of several clouds and find good agreement. These results demonstrate that the extinction-K\,{\sc i} relationship is tight enough to allow linking the radial velocity of the K\,{\sc i} lines to the dust clouds seen in 3D, and that their combination may be a valuable tool in building a 3D kinetic structure of the dense ISM. We discuss limitations and perspectives for this technique.