An investigation was conducted to examine the influence of slip mechanisms on the magnetohydrodynamic (MHD) flow of Casson nanofluid over a permeable stretching sheet. Furthermore, we documented various flow characteristics, including thermal radiation, variable wall thickness, and chemical reaction. By employing the similarity transformation approach, we transformed the partial differential equations governing the flow into nonlinear ordinary equations. Subsequently, we employed the Homotopy Analysis Method (HAM), a well-known semi-analytical technique, to solve these equations, yielding power series solutions for nonlinear differential equations. To demonstrate the effects of velocity, temperature, and concentration profiles, we conducted a parametric study using tables and diagrams. Our numerical results closely align with previous research findings in a comparative sense. Notably, higher values of the velocity slip parameter led to an augmentation in fluid velocity, whereas increased thermal slip values were associated with a reduction in temperature distribution.