A numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity adjacent to a permeable medium. A dominant cross diffusion so called Soret and Dufour effects has been included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. They exhibit both primary and secondary motions when the boundaries are subject to slow rotations. A Galerkin finite element method is employed to solve the emerging multi-physical fluid dynamics problem. The evolution of primary and secondary velocity, primary and secondary angular velocity, temperature and concentration are examined for a variety of parameters which governs the flow. Comparison of the present numerical solutions with the earlier published analytical results shows an excellent agreement, this validating the accuracy of the present numerical method. The current simulations may be applicable to various oscillating rheometry, magnetic rheo-dynamic materials processing systems and rotating MHD energy generator near-wall flows.