It's not a flush, but the easiest thing to do is to suck the fluid out of the reservoir with a turkey baster or something, fill it with new fluid, turn the car on, turn the steering wheel from lock to lock (or very close to), shut the car off and repeat until the fluid looks good.
I'm not sure about the specifics for flushing PS fluid on a B-body, but generally, you disconnect both of the lines from the reservoir. The line from the reservoir to the pump goes into a (large) container of fresh fluid. The other line goes into an empty container. Start the motor and crank the wheel back and forth. The idea is for the pump to suck the new fluid in from the full container and push the old fluid into the empty container. Shut the car off when new fluid comes out of the return line, hook it back up and fill the reservoir. It makes it easier to have a helper to start and shut off the car while you keep an eye on the hoses.
starting the car fully while trying to flush PS fluid will result in big mess and air in system.
Suck Resevoir Dry. Remove return line. It's the smaller one. Add a hose barb and another hose so you can get it to a 5 gallon bucket. cap off return line barb on resevoir with nipple or classic hoseenbolt. Have about 3-4 quarts of PS fluid handy. Fill up resevoir. Go to underhood fuse box. Pull both injector fuses.
Have assistant roll car over for 10-15 seconds at a time, while you add ps fluid to resevoir. Watch the PS fluid coming out of the return line in the bucket. When new fluid comes out you're done. Suck resevoir dry, reattach return hose, fill back up to slighly under capacity, put fuses back in, start car and recheck level.
from Todd Stranczek's great reply in another thread...
Default Flushing Power Steering Fluid
I have flushed mine quite a few times - Best way I have found it to
suction the remote reservoir empty. Remove 3/8" return line and insert a hose barb coupler with about 5 feet of clear tubing from Home Depot on it & use a rubber vacuum cap to temporarily cap the return fitting in the reservoir. Place the other end of the hose in a bucket.
Jack the front end up so the front wheels are off the ground.
Refill the reservoir and continue filling while someone turns the steering wheel lock to lock - until the fluid flows clean - usually between 1 and 2 quarts.
If it is really bad, or you are replacing a failed part – I would recommend holding the end of the clear tubing in the reservoir starting the engine and run it through lock to lock another 5 or six times. This is the return line side so there isn’t a great deal of pressure but I would suggest you zip tie the pushed on hose ends so you don’t make a mess!
Then flush fresh fluid through the system again just like the first time. – When it runs clear connect everything, start the engine and check for leaks. Service as required.
Should be good for another season or two….