Silicone rubber (SR) is one of the most widely used synthetic rubbers owing to its excellent high-temperature resistance and outstanding high-voltage insulation. However, the flammability of SR severely restricts its further promotion and application in fields with high flame-retardancy requirements. In this study, an effective mixing process strategy was proposed for preparing flame-retarding SR/hydroxylated boron nitride (HOBN) nanocomposites using a novel eccentric rotor internal mixer, which could strengthen the hydrogen bond between SR and HOBN through transient normal stress based on volumetric extensional rheology. The strengthening effect of transient normal stress on hydrogen bonds can effectively promote the uniform dispersion, efficient exfoliation, and horizontal orientation of HOBN in the SR matrix. The layer thickness of HOBN was reduced from 200 to 6 nm, and its orientation degree I002/I100 increased from 25 to 112. As expected, the SR/HOBN nanocomposite exhibited excellent flame retardancy with a drastic decrease of 76.4%, 36.0%, 81.7%, and 55.3% in the values of the peak heat release rate, total heat release, smoke production rate, and total smoke production, respectively, compared to neat SR. The flame-retardant mechanism revealed that the physical barrier action of HOBN and the cross-linking reaction between SR and HOBN during combustion showed prominent synergism in the ceramization of the condensed phase to form a compact and adamant protective char layer, thus significantly improving the flame retardancy and smoke suppression of SR. This study provides an efficient and innovative mixing method for the preparation of flame-retardant polymers and will facilitate the development of high-performance rubber processing technology and equipment.