Boron nitride‐based polymer composites possess high thermal conductivity and are commonly used for thermal management. However, the poor interfacial interaction between the fillers and matrix and the random distribution of fillers restrict further improvement of the thermal conductivity and other properties of these composites. Therefore, we propose a strategy to fabricate highly thermally conductive composites with multifunctionalities by interacting boron nitride as the filler with a poly(vinyl alcohol) (PVA) matrix after a ball milling modification, forming a layered nacre‐like structure through vacuum filtration, and hot pressing. The hot‐pressed functionalized boron nitride nanosheets/PVA (HPF‐BNNSs/PVA) composites exhibit a high in‐plane and out‐of‐plane thermal conductivity of 29.4 W/mK and 2.5 W/mK, respectively, at 70 wt% functionalized boron nitride nanosheets (f‐BNNSs) loading. This extraordinary enhancement in thermal conductivity can be ascribed to the formation of an effective thermally conductive network of fillers inside the polymer matrix. Additionally, the HPF‐BNNSs/PVA composites exhibit a low dielectric constant of 3.5, a low dielectric loss of 0.04, high electrical resistivity of 4 × 109 Ω·m, and outstanding mechanical properties (e.g. a tensile strength of 62 MPa and a Young's modulus of 225 MPa) at 70 wt% f‐BNNSs loading. Overall, this study provides a green and facile method to fabricate multifunctional and highly thermally conductive composites for thermal management applications.