In those vehicles that have a removable rear cover, I've always just wiped out the bottom of the pumpkin. None of my vehicles now have a differential with a cover, so I just drain when warm and refill...if I were getting super picky, I might try to flush using new gear oil, but I've never been that picky.
As a data point, every time I've driven the 4 Runner in salt water over the axles, I've changed the gear oil (front and rear differentials) as a precaution. I change it at 30,000 miles otherwise. It doesn't have covers on either diff, just drain and fill plugs. In every case, it has come out looking nearly new - so I don't think that you need to flush anything, just change it.