Easy way to flush;
1, Pay a neighbor kid to steer the wheel back and forth.
2. Remove the return line from the reservoir and add enough hose to go up and over the fender/grille and into a container.
2a. Cap the return nipple on the reservoir.
3. Get a bunch of cheap power steering fluid (not transmission fluid).
4. Remove the belt.
5. Thread a short 3/8" coarse thread bolt into the power steering pump shaft.
6. Grab your cordless drill and fit it with a socket that fits the bolt in the pump.
7. Raise the front end to get the tires off the ground.
8. Rig up a funnel so you can pour the fluid in quickly without making a mess.
9. Fill the reservoir, spin the pump while keeping the funnel full as best you can while the kid turns the wheel back and forth from lock to lock.
10. Continue this procedure until the fluid comes out clean.
11. Drain the remaining fluid.
12. Button the hoses back up but leave the funnel in and the belt off.
13. Put a bottle of Lucas Power Steering Stop Leak in the pump and top up the reservoir with the name brand power steering fluid of your choice.
14. Follow the bleeding procedure from someotherguy except when it says start the engine for a few seconds use the cordless instead. Much easier to control.
15. Thank the kid and send him/her home.
Also consider changing the hoses and adding a magnetic filter too.
P.S. I don't know what magic snake oil is in the Lucas goop but I have had it cure a power steering whine on four of my vehicles. Pour it in and it just goes away.