Using molecular dynamics simulations we investigate the shear-induced rotational dynamics of a Brownian nanographene (hexabenzocoronene) freely suspended in a liquid. We demonstrate that, owing to a finite hydrodynamic slip at the molecular surface, these flat molecules tend to align with a constant orientation angle instead of performing the classical periodic orbits predicted by Jeffery's theory. Results are extracted for different Péclet numbers and compared to the predictions by a theory developed for a rigid axisymmetric particle with orientation confined to the flow-gradient plane. The theory is based on the resolution of a one-dimensional Fokker-Planck equation for the angle φ made by one of the particle's diameters with the flow direction. Remarkably, our results show that the essential features of the three-dimensional orientational statistics of the nanographene are captured by the one-dimensional model, given that the hydrodynamic velocity is closed in terms of the slip length λ. Finally, we explore the situation in which multiple nanographenes are suspended in the liquid, and show that slip results in a reduction in specific viscosity.