We performed molecular dynamics simulations to study the equilibrium and flow properties of a liquid in a nano-channel with confining surfaces coated with a layer of grafted semiflexible polymers. The coverage spans a wide range of grafting densities from essentially isolated chains to dense brushes. The end-grafted polymers were described by a bead spring model with a harmonic potential to include the bond stiffness of the chains. We varied the rigidity of the chains, from fully flexible polymers to rigid rods, in which the configurational entropy of the chains is negligible. The brush-liquid interaction was tuned to obtain a super-hydrophobic channel, in which the liquid did not penetrate the polymer brush, giving rise to a Cassie-Baxter state. Equilibrium properties such as brush height and bending energy were measured, varying the grafting density and the stiffness of the polymers. We also studied the characteristics of the brush-liquid interface and the morphology of the polymer chains supporting the liquid for different bending rigidities. Non-equilibrium simulations were performed, moving the walls of the channel in opposite directions at constant speed, obtaining a Couette velocity profile in the bulk liquid. The molecular degrees of freedom of the polymers were studied as a function of the Weissenberg number. Also, the violation of the no-slip boundary condition and the slip properties were analyzed as a function of the shear rate, grafting density and bending stiffness. At high grafting densities, a finite slip length independent of the shear rate or bending constant was found, while at low grafting densities a very interesting non-monotonic dependence on the bending constant is observed.