We analyse the kinematical properties of the CHEX-MATE (Cluster HEritage project with XMM-Newton – Mass Assembly and Thermodynamics at the Endpoint of structure formation) galaxy cluster sample. Our study is based on the radial velocities retrieved from SDSS-DR18, DESI and NED spectroscopic databases and new data obtained with the 10.4m GTC or the ESO-NTT telescopes. We derive cluster mass profiles for 75 clusters using the MG-MAMPOSSt procedure, which recovers the gravitational potential and the anisotropy profiles from line-of-sight velocities and projected positions of galaxy members. The standard NFW and the Burkert models with flatter cores than NFW both adequately fit the kinematic data, with only marginal statistical preference for one model over the other. An estimation of the mass bias (1 − B) = Msz_500/Mdyn_500(Mampost) is performed from the comparison with SZ-X-ray-calibrated mass estimates, resulting in a value of 0.54 +/- 0.11 when four evidently disturbed clusters are removed from the sample. We assess the dynamical state of the clusters by inferring the Anderson-Darling coefficient (A2) and the fraction of galaxies in substructures (fsub). Except for a few cases, we found relatively low values for A2, suggesting that CHEX-MATE clusters are not too far from relaxation. Moreover, no significant trends emerge among A2, fsub and the difference between the log-masses estimated by MG-MAMPOSSt and by SZ-X-ray. We study the concentration-mass relation for the sample; despite the large scatter, we observe signs of an increasing trend for large-mass clusters, in agreement with recent theoretical expectations. Finally, the analysis of radial anisotropy profiles of member galaxies - stacked in five bins of mass and redshift - reveals that orbits tend to be isotropic at the center and more radial towards the edge, as already found in previous studies. A slight trend of increasing radial orbits at r200 is observed in clusters with larger velocity dispersion.