Graphene is a new material opening up world-changing solutions in many industries, ranging from graphene-infused composites to create more durable, eco-friendly materials such as zero-carbon concrete to nano-ink jet printing of conductive flexible tracks for devices such as flip-phones. Made from just a few atomic layers, the instantaneous dynamics of these plate-like particles in flowing liquids are, experimentally, practically inaccessible. We apply the field of micro-hydrodynamics, the study of colloidal particles in flow, to study theoretically and computationally the flow dynamics of dilute suspensions of graphene in a simple viscous shear flow field. In the infinite Péclet number limit, a rigid platelet with the interfacial hydrodynamic slip properties of graphene does not follow the periodic rotations predicted for classical colloidal particles but aligns itself at a slight inclination angle with respect to the flow. This unexpected result is due to the hydrodynamic slip reducing the tangential stress at the graphene-liquid surface. By analysing the Fokker-Planck equation for the orientational distribution function for decreasing Péclet numbers, we explore how hydrodynamic slip affects the particle’s orientation and macroscopic variables such as the effective viscosity. We find that hydrodynamic slip can dramatically change the average particle’s orientation and effective viscosity. For example, the effective viscosity of a dilute or semi-dilute suspension of graphene platelets is predicted to be smaller than the base fluid under certain flow conditions for typical slip length values.