This work studied the individual and combined addition of natural (MMT-Na) and modified (MMT-30B) nanoclays, and carbon nanotubes (CNTs) to a poly (hexamethylene isophthalamide co-terephthalamide) (aPA)/styrene-ethylene/ butylene-styrene (SEBS) blend grafted with maleic anhydride. Their effects on the blend's morphology, thermo-mechanical properties, and flammability were evaluated. Morphological analysis showed that both clays were located in the aPA matrix, with the MMT-Na as agglomerates and the MMT-30B intercalated with exfoliated regions. The CNTs were dispersed and randomly oriented in the aPA matrix. Data obtained through dynamic-mechanical analysis (DMA) showed that adding 1.0% MMT-30B and 1.0% CNT increased the storage modulus (E') by 26% and 27%, respectively, while adding both 0.5% MMT-30B and 0.5% CNT increased E' by 38%, suggesting synergy between the nanoparticles related to mechanical properties. Regarding flammability, since the first burn timing (t1) could not be obtained, none of the samples could be classified according to the UL94 standard. However, qualitatively, a better flammability performance was noticed for the nanocomposites than for the pure blend.