While the phonon hydrodynamic regime has recently been highlighted experimentally in graphite films, the understanding and modeling of heat transport along their basal plane remain elusive. From first-principles-based modeling, we predict a significant influence of the surface roughness on basal-plane thermal conductivity due to the collective phonon drift. The occurrence condition of the phonon Knudsen minimum is also shown to strongly depend on the surface roughness. We summarize the basal-plane heat transport along graphite thin films into coherent and incoherent regimes and also present a speculation for the recently observed anomalous thickness-dependent thermal conductivity. Our work provides guidance for the experimental explorations of phonon hydrodynamics in graphitic micro-and nanostructures in the future.