The HD 100546 disc represents a particularly interesting target to study dynamical interactions as various features have been observed in the dust and gas, that provide direct and indirect evidence for planet formation. In this work we analyse the gas kinematics of five molecular CO emission lines (12CO 7-6, 3-2, 2-1, 13CO 2-1, C18O 2-1) observed with ALMA in HD 100546 with the Discminer package, to reveal deviations from Keplerian rotation and substructures in the peak intensity and line width. Aside from modeling the full cube we also conduct runs where the blue- and re-shifted sides are modelled separately to search for possible asymmetries. Our analysis yields prominent kinematical spiral features in all five lines on large scales of the disc and we reproduce their morphology with both a linear and logarithmic parametrization. We find that the emission from the red-shifted side is coming from higher disc layers than on the blue-shifted side, with the asymmetry being especially pronounced for the higher 12CO transitions. The pitch angles of the spirals are consistent with Lindblad spirals driven by an embedded companion inside of 50 au and they suggest a dynamical mechanism rather than gravitational instabilities. They decrease closer to the midplane, which matches the predictions of Juhasz & Rosotti (2018). We further find indications of a planet around 100-150 au, where a tentative dip in the integrated intensity profile of 13CO 2-1 is present and pressure minima are observed in the azimuthal velocity. For the first time, we detect meridional flows in this region, which coincide with the dust gap found by Fedele et al. 2021. The asymmetry in the emission heights may be a result of infall from the disc's environment. Another explanation is provided by a warped inner disc, casting a shadow onto one side.