Flexible graphene field-effect transistors (GFETs) are fabricated with graphene channels fully encapsulated in hexagonal boron nitride (hBN) implementing a self-aligned fabrication scheme. Flexible GFETs fabricated with channel lengths of 2 μm demonstrate exceptional room-temperature carrier mobility (μFE = 10 000 cm2 V-1 s-1), strong current saturation characteristics (peak output resistance, r0 = 2000 Ω), and high mechanical flexibility (strain limits of 1%). These values of μFE and r0 are unprecedented in flexible GFETs. Flexible radio frequency FETs (RF-FETs) with channel lengths of 375 nm demonstrate μFE = 2200 cm2 V-1 s-1 and r0 = 132.5 Ω. Unitycurrent gain frequencies, fT, and unitypower gain frequencies, fmax, reach 12.0 and 10.6 GHz, respectively. The corresponding ratio of cutoff frequencies approaches unity (fmax/fT = 0.9), a record value for flexible GFETs. Intrinsic fT and fmax are 29.7 and 15.7 GHz, respectively. The outstanding electronic characteristics are attributed to the improved dielectric environment provided by full hBN encapsulation of the graphene channel in conjunction with an optimized, self-aligned device structure. These results establish hBN as a mechanically robust dielectric that can yield enhanced electronic characteristics to a diverse array of graphene-based flexible electronics.