2003 Chevy Silverado rear end chatter

You probably don't need a flush, but pull the rear diff cover off, drain all the gear oil, use a gasket on the cover, then I recommend replacing with Mobil 1 Synthetic gear oil AND a bottle of limited slip diff lube from a GM dealer. This should be done every 30-40K miles or so, so you are overdue. If you buy a new cover with a drain plug, then you won't have to pull the whole cover off again. When you pull the cover off, you can check for any worn gears, metal in the bottom, damage, etc. Mobil 1 is spendy, but GOOD.