Graphene transistors using hexagonal boron nitride as the gate dielectric are implemented on mechanically flexible polyimide films. Current saturation is observed for the first time in graphene transistors on a plastic substrate. An atomically smooth insulating surface is achieved with the proposed capture-release process and two-step annealing process, resulting in subnanometer surface roughness. The device shows strong electrical performance: Extracted mobility exceeds 2300 cm2/V·s for both electron and hole transport, and drive current is over 300 μS/μm. This transport symmetry affords frequency doublers with high spectral purity and a conversion gain of - 29.5 dB and output power of -22.2 dBm, representing the highest performance for graphene transistors on flexible substrates.