We study the velocity field of umbral dots at a resolution of 0.14. Our analysis is based on full Stokes spectropolarimetric measurements of a pore taken with the CRISP instrument at the Swedish 1-m Solar Telescope. We determine the flow velocity at different heights in the photosphere from a bisector analysis of the Fe I 630 nm lines. In addtion, we use the observed Stokes Q, U, and V profiles to characterize the magnetic properties of these structures. We find that most umbral dots are associated with strong upflows in deep photospheric layers. Some of them also show concentrated patches of downflows at their edges, with sizes of about 0.25, velocities of up to 1000 m/s, and enhanced net circular polarization signals. The downflows evolve rapidly and have lifetimes of only a few minutes. These results appear to validate numerical models of magnetoconvection in the presence of strong magnetic fields.