Aqueous miscible organic layered double hydroxides (AMO-LDHs) can act as organophilic inorganic flame retardant nanofillers for unmodified non-polar polymers. In this contribution, AMO [Mg3Al(OH)8](CO3)0.5·yH2O LDH–oxidized carbon nanotube (AMO-LDH–OCNT) hybrids are shown to perform better than the equivalent pure AMO-LDH. A synergistic effect between the AMO-LDH and OCNT was observed; this endows the hybrid material with enhanced flame retardancy, thermal stability, and mechanical properties. The thermal stability of polypropylene (PP) was significantly enhanced by adding AMO-LDH–OCNT hybrids. For PP mixed with AMO-LDH–OCNT hybrids to produce a composite with 10 wt% LDH and 2 wt% OCNT, the 50% weight loss temperature was increased by 43 °C. Further, a system with 10 wt% of AMO-LDH and 1 wt% OCNT showed a peak heat release rate (PHRR) reduction of 40%, greater than the PHRR reduction with PP/20 wt% AMO-LDH (31%). The degree of dispersion (mixability) between AMO-LDH and OCNT has a significant effect on the flame retardant performance of the hybrids. In addition, the incorporation of AMO-LDH–OCNT hybrids led to better mechanical properties, such as higher tensile strength (27.5 MPa) and elongation at break (17.9%), than those composites containing only AMO-LDH (25.6 MPa and 7.5%, respectively).