When draining the black tank, most of the liquid can run out and leave behind a mound of solids blocking the drain line. Each unit will be different and depends on how level it is and how it is plumbed. By adding sufficient water to the black tank with the flusher, it will fill enough to push out the blockage and have a rush of water behind it. Just monitor it the first few times you dump it and you will learn how much water it takes to flush. With my particular unit, I have found that if I raise the front as high as I can get it, it will flush easier.
It's sounding like nothing is coming out of the sewer outlet while you're running the black tank flush.
If your black tank valve leaks a little bit, the black water can drain out slowly when you're not dumping the tank, especially if you leave the sewer line hooked up with gray valves open. As Hoefler noted, this results in a buildup of solids and paper in the bottom of the tank. When you begin flushing, it can move to the gate valve opening and block it until there's enough pressure to force it out with a rush of water behind it.
If you get some sense of the water flow coming out of the campground, you can run a timer on your cell phone while using the black tank flush. At 5 gallons/minute going into a 45 gallon tank (if that's what you have), you can run the black tank flush for 5 minutes without too much risk of overfilling, even if there's still water in the black tank. Somewhere in that 5 minutes, the blockage should clear. Be careful: if you overfill the black tank, things can get ugly.
If it doesn't clear, you'll need to backflush from the sewer hose. One way is with a
Flush King adapter like this. If you don't have one, you can try filling the sewer hose with water from the far end (don't contaminate your hose), and hold it above your head to let gravity backflush the clog away from the valve.
During all these operations, it's a good idea to keep your gray tank valves closed.
