You don't *have* to, but things stay cleaner if you let the tank fill and then empty it. The rush of water scours the tank and pushes out any food bits that may be festering on the bottom of the tank.
Letting the black tank fill before emptying is actually very important for the same reason. Let it fill up, empty it, flush it, and then empty the gray tank so the gray water flushes the black tank ick out of your sewer hose.
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Silver Meteor - 2009 Airstream Classic Limited 34
2016 RAM 2500 Laramie Crew Cab 4x4, Cummins TurboDiesel