Bummer!Flushing the brakes requires the complete system. Not just the reservoir. You'll be sucking in the old stuff with the new stuff every time you use the brake pedal.
Best thing to do is have a shop that has a machine to flush the system. They can force fresh fluid through the system with all 4 valves open.
However, You can use a vacuum pump and suck the fluid at the valves. Just make sure the reservoir stays full. Don't let it dry out.