The thermally conductive structural film adhesive not only carries large loads but also exhibits excellent heat-transfer performance, which has huge application prospects. Herein, a novel epoxy (Ep) thermally conductive structural film adhesive was prepared using polyphenoxy (PHO) as the toughening agent and film former, boron nitride (BN) nanosheets as the thermally conductive filler, and polyester fabric as the carrier. When the amount of PHO in the epoxy matrix was 30 phr and the content of nano-BN was 30 wt.% (Ep/PHO30/nBN30), the adhesive resin system showed good film-forming properties, thermal stability, and thermal conductivity. The glass transition temperature of Ep/PHO30/nBN30 was 215 °C, and the thermal conductivity was 209.5% higher than that of the pure epoxy resin. The Ep/PHO30/nBN30 film adhesive possessed excellent adhesion and peeling properties, and the double-lap shear strength at room temperature reached 36.69 MPa, which was 21.3% higher than that of pure epoxy resin. The double-lap shear strength reached 15.41 MPa at 150 °C, demonstrating excellent high temperature resistance. In addition, the Ep/PHO30/nBN30 film adhesive exhibited excellent heat-aging resistance, humidity, and medium resistance, and the shear strength retention rate after exposure to the complicated environment reached more than 90%. The structural film adhesive prepared showed excellent fatigue resistance in the dynamic load fatigue test, the double-lap shear strength still reached 35.55 MPa after 1,000,000 fatigue cycles, and the strength retention rate was 96.9%, showing excellent durability and fatigue resistance.