Rather than a splitter and two hoses running to the RV, I just use the outside shower hose in the convenience center when I need to flush the black tank. I have quick disconnects on the shower hose and the black tank flush connection. That way it takes no time at all to connect, flush, and disconnect, all while sitting right there and not walking away (when bad things tend to happen).
P.S. I use quick disconnects on my shore water hoses too. The quick disconnects on the shower hose are reversed from the quick disconnects on the water hoses. That way you can't accidentally connect the shore water to the black tank flush or the shower hose to the shore water inlet.
Vs. this style
