Unlikely that you would need them all open. The tank flush is only going to be hooked directly up to the black tank.
I didn't get any instructions to leave my valve open. I understand why (forgetting and overflowing the tank would be a horrifying nightmare). I close my valves and then set a timer on my phone while I'm running it AND stay outside on that side of the camper to remind myself.
I never realized I was quite so spastic- but I normally dump my black tank, close the value, run the flush for 6 minutes, then flush and then repeat the fill/flush cycle 2 more times at 5 minutes and 4 minutes of filling each. I keep a clear elbow on my sewer outlet so that I can see the "water" and make sure it's running clear before calling it done for the black tank. After the black is done, I empty the gray tanks.