Flexible substrates that host electronic components are an essential part of flexible electronics. The continuing miniaturization of these electronics requires flexible substrates with excellent flexibility, high thermal conductivity, and low dielectric constant. However, to combine these intended properties remains a daunting challenge. Here, a flexible fibrous epoxy substrate fabricated by an electrospinning technique is reported, which exhibits excellent flexibility, high thermal conductivity, and low dielectric constant. The thermal conductivity can be tuned by varying the diameter of fibers and can reach values as high as 0.8 W m −1 K −1 , which is about three times higher than that of casted epoxy substrate fabricated by spin‐coating. This excellent performance is attributed to polymer molecular chain alignment and fibrous structure that are formed during electrospinning. Demonstrative applications suggests its broad potential uses in future flexible electronics.