Due to the rapid development of miniaturization, portability, and flexibility of electronic devices, the demand for polymer composites with high thermal conductivity, mechanical flexibility, and electrical insulation has increased significantly. In this work, we report a boron nitride nanosheet (BNNS)-cellulose nanocrystal (CNC)/polydimethylsiloxane (PDMS) composite with excellent thermal conductivity and superior mechanical flexibility prepared by ultrasonic-assisted forced infiltration. Different BNNS proportions in the composites system would lead to different thermal properties. When the mass ratio of BNNS to CNC reaches 25:1, the BNNS-CNC(25:1)/PDMS composite attains a high thermal conductivity of 7.309 W/(m·K), 2607% higher than that of pure PDMS matrix. In addition, the BNNS-CNC/PDMS composites also have excellent dielectric properties, electrical insulation, and mechanical flexibility. The PDMS composites reported in this paper have strong potential in thermal management applications for electronic devices.