That lever (It says "Tank Fill Power
Fresh" not flush), only controls your fresh water, it has absolutely nothing to do with your black tank flush..
When the lever is in the horizontal "Normal Flow" position as shown in your photo, fresh water (from the hose that is connected to a faucet to your "City Water Connection" the middle one in the convenience center), is directed to the 5er's plumbing system, sink faucets, shower, toilet, etc...
When you turn the knob to the vertical "Fill" position, the city water supply fills your fresh water tank. Watch your tank gauges carefully when when using this, and turn it off when the indicator light says the fresh tank is full. If you forget to turn it off, you can rupture your fresh water tank with too much pressure.
To flush your black tank, connect a hose that you don't use for potable water, a grey water hose, to the bottom connection that is directly under the "City Water Supply" connection. Just turn on the water faucet after you have opened the black tank dump valve, and the black tank flush does it's thing. If you then close the dump valve and use the flush connection to fill the black tank up a bit after your initial dump to get a little better flush, don't let it fill up the black tank too much, or forget it, because you can rupture the black tank that way too, or blow poo water out of the roof vent.
Did you ever see that movie with Robin Williams called "RV"?
https://youtu.be/uHgRmR024BE