Low-cost flexible microwave circuits with compact size and light weight are highly desirable for flexible wireless communication and other miniaturized microwave systems. However, the prevalent studies on flexible microwave electronics have only focused on individual flexible microwave elements such as transistors, inductors, capacitors, and transmission lines. Thinning down supporting substrate of rigid chip-based monolithic microwave integrated circuits has been the only approach toward flexible microwave integrated circuits. Here, we report a flexible microwave integrated circuit strategy integrating membrane AlGaN/GaN high electron mobility transistor with passive impedance matching networks on cellulose nanofibril paper. The strategy enables a heterogeneously integrated and, to our knowledge, the first flexible microwave amplifier that can output 10 mW power beyond 5 GHz and can also be easily disposed of due to the use of cellulose nanofibril paper as the circuit substrate. The demonstration represents a critical step forward in realizing flexible wireless communication devices.