Using equilibrium and non-equilibrium molecular dynamics simulations, we study the flow of argon fluid above the critical temperature in a planar nanochannel delimited by graphene walls. We observe that, as a function of pressure, the slip length first decreases due to the decreasing mean free path of gas molecules, reaches the minimum value when the pressure is close to the critical pressure, and then increases with further increase in pressure. We demonstrate that the slip length increase at high pressures is due to the fact that the viscosity of fluid increases much faster with pressure than the friction coefficient between the fluid and the graphene. This behavior is clearly exhibited in the case of graphene due to a very smooth potential landscape originating from a very high atomic density of graphene planes. By contrast, on surfaces with lower atomic density, such as an (100) Au surface, the slip length for high fluid pressures is essentially zero, regardless of the nature of interaction between fluid and the solid wall.