This paper aims to investigate the effects of the Ekman-Hartmann boundary layer on rotating magnetohydrodynamics (MHD) within cylindrical domains, focusing on constructing approximate solutions within the boundary layer. We employed the multiscale analysis method to derive the approximate solutions, emphasizing the solutions at the cylinder's corners and lateral boundaries. Furthermore, we rigorously examined the asymptotic behavior of the rotating MHD flow in the limit case, proving its convergence to a two-dimensional damped and rotating dynamical system. These findings revealed the significant impact of high-speed rotation and strong magnetic fields on the structure and flow characteristics of the boundary layer, providing new insights into the dynamics of rotating MHD flows.