In this experimental work, the flammability performance of sisal/epoxy and hemp/epoxy composites infused with graphene nanocomposites at varying weight percentages was studied. The composite samples were fabricated using the hand lay-up technique, and the samples were subjected to the UL-94 test in both vertical and horizontal directions. The results revealed that sisal/epoxy samples exhibited a V-1 rating, which was attributed to the absence of dripping. However, the hemp/epoxy samples showed dripping, and resulted in a V-2 rating. Further, the burn time ranged from 170 to 210 s for all composite samples. A decrease in burn time was observed for all sisal-based composite samples with varying graphene content, whereas hemp-based samples exhibited a significant reduction in burn time only at 3 wt% of graphene. Based on these observations, sisal-based composite samples can be proposed for fire-sensitive applications due to their superior flammability resistance behavior.