The magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid is investigated numerically in a channel of either rectangular or semi-infinite cross-section with several types of boundary conditions involving walls of variable conductivity in the presence of hydrodynamic slip. The flow is fully developed and driven by a constant pressure gradient in the axial direction under a uniform external inclined magnetic field. The governing differential equations coupled in velocity and induced magnetic field are discretized by a direct boundary element method in which the employed fundamental solution is able to treat the equations in their original coupled form. Thus, the resulting system of equations involving the unknown values of velocity, induced magnetic field and their normal derivatives, according to the adopted boundary conditions, only on the boundary of the duct is small in size and is solved at one stroke with no iteration. The numerical simulations are carried out for several values of slip length, wall conductivity parameter, Hartmann number and the inclination angle of the external magnetic field. The results are visualized basically in terms of velocity and induced magnetic field distributions along the vertical centerline of the cavity to analyze the influence of the slip on the system of magnetohydrodynamic flow.