This study presents a systematic investigation of thermal transport properties in a novel class of carbon-based graphene-like materials (AKCs). Through first-principles calculations combined with the phonon Boltzmann transport equation and machine-learning potential, we analyzed the lattice thermal conductivity and its microscopic mechanisms in three structures: AKC60, AKC33, and AKC41. The research reveals that these materials exhibit significant in-plane thermal conductivity at room temperature (191.0 W/m·K, 122.6 W/m·K, and 248.3 W/m·K, respectively), though an order of magnitude lower than that of graphene. Through detailed analysis of phonon dispersion relations, group velocities, three-phonon scattering phase space, and Grüneisen parameters, we uncovered the physical origins of AKCs' relatively lower thermal conductivity. The findings indicate that despite AKC60's larger primitive cell, its better preservation of graphene's honeycomb structure leads to superior harmonic properties, resulting in higher thermal conductivity than that of AKC33 with its smaller primitive cell. These discoveries provide valuable guidance for AKCs' applications in future electronic devices.