The continuous evolution toward semiconductor technology in the “more-than-Moore” era and rapidly increasing power density of modern electronic devices call for advanced thermal interface materials (TIMs). Here, we report a novel strategy to construct flexible polymer nanocomposite TIMs for advanced thermal management applications. First, aligned polyvinyl alcohol (PVA) supported and interconnected 2D boron nitride nanosheets (BNNSs) composite fiber membranes were fabricated by electrospinning. Then, the nanocomposite TIMs were constructed by rolling the PVA/BNNS composite fiber membranes to form cylinders and subsequently vacuum-assisted impregnation of polydimethylsiloxane (PDMS) into the porous cylinders. The nanocomposite TIMs not only exhibit a superhigh through-plane thermal conductivity enhancement of about 10 times at a low BNNS loading of 15.6 vol % in comparison with the pristine PDMS but also show excellent electrical insulating property (i.e., high volume electrical resistivity). The outstanding thermal management capability of the nanocomposite TIMs was practically confirmed by capturing the surface temperature variations of a working LED chip integrated with the nanocomposite TIMs.