Nanofluids based on vegetal oil with different wt.% of carbon nanotubes (CNT), hexagonal boron nitride (h-BN), and its hybrid (h-BN@CNT) were produced to investigate the effects of these nano-additives on the thermal conductivity and rheological properties of nanofluids. Stable suspensions of these oil/nanostructures were produced without the use of stabilizing agents. The dispersed nanostructures were investigated by SEM, EDS, XRD, and XPS, while the thermal conductivity and rheological characteristics were studied by a transient hot-wire method and steady-state flow tests, respectively. Increases in thermal conductivity of up to 39% were observed for fluids produced with 0.5 wt.% of the hybrid nanomaterials. As for the rheological properties, it was verified that both the base fluid and the h-BN suspensions exhibited Newtonian behavior, while the presence of CNT modified this tendency. This change in behavior is attributed to the hydrophobic character of both CNT and the base oil, while h-BN nanostructures have lip-lip “bonds”, giving it a partial ionic character. However, the combination of these nanostructures was fundamental for the synergistic effect on the increase of thermal conductivity with respect to their counterparts.