We present a Bayesian phase-space reconstruction of the cosmic large-scale matter density and velocity fields from the SDSS-III Baryon Oscillations Spectroscopic Survey Data Release 12 (BOSS DR12) CMASS galaxy clustering catalogue. We rely on a given $Lambda$CDM cosmology, a mesh resolution in the range of 6-10 $h^{-1}$ Mpc, and a lognormal-Poisson model with a redshift dependent nonlinear bias. The bias parameters are derived from the data and a general renormalised perturbation theory approach. We use combined Gibbs and Hamiltonian sampling, implemented in the textsc{argo} code, to iteratively reconstruct the dark matter density field and the coherent peculiar velocities of individual galaxies, correcting hereby for coherent redshift space distortions (RSD). Our tests relying on accurate $N$-body based mock galaxy catalogues, show unbiased real space power spectra of the nonlinear density field up to $ksim0.2, h$ Mpc$^{-1}$, and vanishing quadrupoles down to $rsim20,h^{-1}$ Mpc. We also demonstrate that the nonlinear cosmic web can be obtained from the tidal field tensor based on the Gaussian component of the reconstructed density field. We find that the reconstructed velocities have a statistical correlation coefficient compared to the true velocities of each individual lightcone mock galaxy of $rsim0.68$ including about 10% of satellite galaxies with virial motions (about $r=0.75$ without satellites). The power spectra of the velocity divergence agree well with theoretical predictions up to $ksim0.2,h,{rm Mpc}^{-1}$. This work will be especially useful to improve, e.g. BAO reconstructions, kinematic Sunyaev-Zeldovich (kSZ), integrated Sachs-Wolfe (ISW) measurements, or environmental studies.
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