[JRTJH]

When you do the "critical analysis" of pumping shower gray water into the black tank via the black tank flush system, you will find that there is a lot of damage you can do, not only to the pump you use, but also to the black tank flush system.

First, soap scum, human hair and even the dirt/sand that is in shower water will foul the pump diaphragm and any valves that might be in the pump, depending on the style pump you use.

Second, on some black tank flush systems there is a rotating spray head inside the tank. It may foul with human hair and soap scum. Then there's the anti-siphon valve through which you'll be pumping that "scummy water". As the weakest link in the system, no telling what damage you might do. Finally, there's a backflow valve in the water inlet connection. It's a plastic, spring loaded "plug" that opens to allow water into the black tank flush system and "springs closed" to prevent contamination (back pressure leaking) from any dribbles, should the system "burp" or "build pressure". Imagine what human hair balls, soap scum and the grit from the gray tank would (could) do to that valve. Once it's leaking, black tank contents that might get past the contaminated or damaged anti-siphon valve would (could) contaminate the side of your trailer and/or the fresh water hose, once you decide to use the system "for what it was designed".....

I'd think using the black tank flush system to pump dirty water into the trailer black tank is probably not a good idea for system reliability and/or longevity