Flexible circuit board materials with low dielectric constant (εr), low dielectric loss (tanδ) and high thermal conductivity (TC) were highly desired for high-frequency and high-speed electronic equipment. Herein, hexagonal boron nitride (h-BN) sheets were filled into highly elastic styrene ethylene butylene styrene (SEBS) matrix and oriented along in-plane direction regularly by hot-pressing method. SEBS/h-BN films exhibited high TC and outstanding flexibility except relatively high tanδ and water absorption. The sandwich structure was designed utilizing pure cyclic olefin copolymer (COC) films as outer surface layers and SEBS/h-BN film as interlayer. The introduction of COC films reduced the tanδ and water absorption of SEBS/h-BN film without reducing original TC obviously. Hybrid SEBS/COC/BN films owning the same components with sandwich-structure films were also fabricated to verify the advantages of designed structure. Sandwich-structure films always kept good flexibility and exhibited low εr (2.7–3.6), low tanδ (<1 × 10−3, 10 GHz), high TC (3.8–17.6 W m−1 K−1) and low water absorption (<0.1%). These films were also fabricated into flexible copper clad laminates and patch antenna operated in sub-6G band. The antenna exhibited a return loss of −32.8 dB and a gain of 7.04 dBi. The flexible substrates show great potential and satisfy large-scale production demand in high TC flexible circuit board materials field.