A theoretical and computational study of a magnetohydrodynamic and three-dimensional flow over a variable thickness sheet (slendering sheet) with Cattaneo-Christov heat flux is presented. The Williamson slip is considered at the modified boundary conditions. The Williamson slip model is employed which is representative of certain industrial polymers. The non-dimensional, transformed boundary layer equations for momentum, energy and species diffusion are transformed with appropriate boundary conditions. The non-linear ordinary differential equations (ODEs) are solved using the Runge-Kutta-Fehlberg integration method. Validation of the numerical solutions is achieved via bench marking with earlier published work. The influence of Williamson slip suppresses the momentum boundary layers thickness and enhances the thermal solutal boundary layer thickness. Graphically studied thermal relaxation parameter, wall thickness parameter, porosity parameter, Brownian motion and thermophoresis parameters.