Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.