Aims. The co-evolution of galaxies and supermassive black holes (SMBHs) requires that some sort of feedback mechanism is operating during the active galactic nuclei (AGN) phases. AGN driven winds are the most likely candidates for such feedback mechanism, but direct observational evidence of their existence and of their effects on the host galaxies are still scarce and their physical origin is still hotly debated. Methods. X-Shooter observations of a sample of X-ray selected, obscured quasars at z ∼ 1.5, selected on the basis of their observed red colors and X-ray-to-optical flux ratio, have shown the presence of outflowing ionized gas identified by broad [OIII] emission lines in 6 out of 8 objects, confirming the efficiency of the selection criteria. Here we present slit-resolved spectroscopy for the two brightest sources, XID2028 and XID5321, to study the complex emission and absorption line kinematics. Results. We detect outflow extended out to ∼10 kpc from the central black hole, both as blueshifted and redshifted emission. Interestingly, we also detect kpc scale outflows in the [OII] emission lines and in the neutral gas component, traced by the sodium D and magnesium absorption lines, confirming that a substantial amount of the outflowing mass is in the form of neutral gas. Conclusions. The measured gas velocities and the outflow kinetic powers, inferred under reasonable assumptions on the geometry and physical properties of these two systems, favor an AGN origin for the observed winds.