Extreme confinement in nanochannels results in unconventional equilibrium and flow behavior of polymers. The underlying flow physics dictating such paradigms remains far from being understood and more so if the confining substrate is composed of two-dimensional materials, such as graphene. In this study, we conducted systematic molecular dynamics simulations to explore the effect of wettability, confinement, and chain length on polymer flow through graphene-like nanochannels. Altering the wetting properties of these membranes that structurally represent graphene results in substantial changes in the behavior of polymers of disparate chain lengths. Longer hydrocarbon chains (n-dodecane) exhibit negligible wettability-dependent structuring in narrower nanochannels compared to shorter chains (n-hexane) culminating in higher average velocities and interfacial slippage of n-dodecane under less wettable conditions. We demonstrate that the wettability compensation comes from chain entanglement attributed to entropic factors. This study reveals a delicate balance between wettability-dependent enthalpy and chain-length-dependent entropy, resulting in a unique nanoscale flow paradigm, thus not only having far-reaching implications in the superior discernment of polymeric flow in sub-micrometer regimes but also potentially revolutionizing various applications in the oil industry, including innovative oil transport, oil extraction, ion transport polymers, and separation membranes.