Commercial thermally conductive dielectric materials used in electronic packaging typically exhibit thermal conductivities (κ) ranging from 0.8 to 4.2 W m−1 K−1. Hexagonal boron nitride (h-BN) flakes are promising thermally conductive materials for the thermal management of next-generation electronics. These electrically insulating yet thermally conducting h-BN flakes can be incorporated as thermal fillers to impart high κ to polymer-based composites. A cellulose-based composite embedded with few-layer h-BN (FLh-BN) flakes, achieving a κ ≈ 21.7 W m−1 K−1, prepared using a cost-effective and scalable procedure is demonstrated. This value is >5 times higher than the κ observed in composites embedded with bulk h-BN (Bh-BN, κ ≈ 4.5 W m−1 K−1), indicating the benefits of the superior κ of FLh-BN on the κ of h-BN polymer composites. When applied as a paste for thermal interface material (TIM), the FLh-BN composite can reduce the maximum temperature (Tmax) by 24.5 °C of a heating pad at a power density (h) of 2.48 W cm−2 compared to Bh-BN composites at the same h-BN loading. The results provide an effective approach to improve the κ of cellulose-based thermal pastes for TIMs and demonstrate their viability for heat dissipation in integrated circuits (ICs) and high-power electronic devices.