A flow control assembly can include a pilot-operated valve and a pilot control valve. The pilot-operated valve includes a closure element between inlet port and outlet ports of the pilot-operated valve and an actuating element adjacent to the closure element. The closure element can move between an open position allowing fluid flow between the inlet and outlet ports and a closed position preventing fluid flow between the inlet and outlet ports. A pilot pressure communicated to the actuating element can cause the actuating element to apply force that moves the closure element to the open position. The pilot control valve can include a closure element between inlet port and outlet ports of the pilot control valve. Communicating an actuation pressure to the closure element of the pilot control valve can open the pilot control valve. Opening the pilot control valve can allow communication of pilot pressure to the pilot-operated valve.