Despite abundant studies on gas barrier, viscoelastic, and flammability properties of polymer nanocomposites, comprehensive understandings of these performances and their relationships are still lacking. We herein attempt to gain deep insights into the performances by creating several polymer nanocomposites by incorporating three types of nanoparticles, nanoclay (Clay), carbon nanotubes (CNTs), and reduced graphene nanoplates (RGO), into polypropylene (PP). The oxygen permeability, viscoelasticity, and flammability measurements demonstrate that RGO can lead to much more reduction in the gas permeability (by similar to 73%) and flammability (peak heat release rate (PHRR) reduction by similar to 78%), as well as a higher storage modulus and melt viscosity of polymer matrix relative to clay and CNTs at the same loading (1.0 wt %) due to its higher aspect ratio. Clay performs better than CNTs in terms of gas barrier property due to its lamellar structure while behaves worse than CNTs in terms of increasing the melt viscosity and reducing flammability of polymers. Most important, there is a nearly line correlation among these properties for all polymer nanocomposites despite some deviations.