The development of flexible electronics operating at radio-frequencies (RF) requires materials that combine excellent electronic performance and the ability to withstand high levels of strain. In this work, we fabricate graphene field-effect transistors (GFETs) on flexible substrates from graphene grown by chemical vapor deposition (CVD). Our devices demonstrate unity-current-gain frequencies, f(T), and unity-power-gain frequencies, f(max), up to 10.7 GHz and 3.7 GHz, respectively, with strain limits of 1.75%. These devices represent the only reported technology to achieve gigahertz-frequency power gain at strain levels above 0.5%. As such, they demonstrate the potential of CVD graphene to enable a broad range of flexible electronic technologies which require both high flexibility and RF operation.