The turbine rotor blade with an aft flowing serpentine flow cooling circuit that discharges into a trailing edge cooling circuit and then into a row of exit cooling slots to cool the trailing edge, in which a vortex cooling chamber is formed in the blade platform and root section just below the trailing edge of the airfoil, the vortex chamber receiving cooling an bled off from the root turn of the serpentine flow circuit to produce a vortex flow of the cooling air and provide cooling for this section of the blade root. The vortex cooling air is then discharged through a row of exit cooling holes that open onto the side edge of the platform on the pressure side to cool the blade mate-face and to purge an aft rim cavity.