This is what I have always done to rinse out the BW tank from the Gray tank water.
Empty BW tank. Grab the drain hose and lift it up and higher than the BW tank. With the hose high, reach in and pull the Gray tank flush handle. the Gray water, with soap from sink dish water will flow into the BW tank. Allow 1/4 of the GW to flow into the BW tank. Close GW tank valve and drop the drain hose to allow the BW tank to 'flush out'. Repeat twice more and on the last time leave the GW valve open when lowering the hose to allow all of the water from both tanks to flow out.
2013 Forest River Salem Hemisphere SBT312QBUD
2001 CrewCab F-250 7.3 PowerStroke Diesel
SuperChip, BTS transmission, 6.0 Trans Cooler