Spin-polarized transport through a quantum dot strongly coupled to ferromagnetic electrodes with non-collinear magnetic moments is analyzed theoretically in terms of the non-equilibrium Green function formalism. Electrons in the dot are assumed to be coupled to a phonon bath. The influence of electron-phonon coupling on tunnelling current, linear and nonlinear conductance, and on tunnel magnetoresistance is studied in detail. Variation of the main Kondo peaks and phonon satellites with the angle between magnetic moments of the leads is analyzed.