I'm doing a flush as well. Pulling the reservoir and getting the internal screen is first order of business. I suspect it will take three flush, one qt. a time driving for the week in between each flush. At least that what the last under maintained rig took.
FWIW: Steering Flush & Cleaning
Once steering pump noise quiets down it helps isolate other sound from fan clutch, idler & tensioner bearings and compressor.
Is your PS pump making noise all the time, just during turns, or chirping at start up?