I have a generic version of the Flush King and use it all the time. Here is how I do it, and I have found this is probably the best method. As stated by the previous poster, you do not need to flush out the gray tank.
I'm assuming your camper has 2 tanks and both tanks drain into one outlet. Each tank has it own release valve. Here's a set of photos of my camper and "reverse flusher" and how I use it. I think you will find this the most effective too. After doing it the first time, it won't be so confusing. I lettered the 3rd photo to make the steps easier to follow. I'm also assuming your Flush King comes with the clear section. This is really the most important part of the system, so you can see what is coming out and when it quits draining.


Here is the same photo with a lettering system to identify each item:
Valve A is the Flush King valve
Valve B is the Black tank valve
Valve C is the Gray tank valve
Item D is the garden hose and the twist knob to direct the water from the hose up and back into the tanks, down the drain hose only, or completely off.

To start this process, you need liquids in both tanks. The more you have in the gray tank, the better this works. Also, you really do not need the garden hose at all. It's not necessary, but I'll address that later.
Attach the "Reverse Flusher" and close all valves.
First, open Valve A (Flush King valve)
Second, open Valve B (Black tank) and let the black tank run until it's empty. You can see when it's empty because of the clear section. You can also see the contents coming out. You'll be surprised what happens next!
Third, when the black tank ends, close Valve A (Flush King). Leave Valve B open (black tank), and open Valve C (gray tank). Because the black tank is empty, the gray water will force itself into the black tank, filling it with sine if the water from the gray tank. Leave Valve C open for only about 10 seconds then close it. You don't want the black tank contents to flush back into the gray. So, only a few seconds, then close it.
The sudden force of the gray tank pushing backwards into the black tank will beat up any remaining contents in the black. The backward rush will loosen everything remaining.
With the gray tank closed (Valve C), now open Valve A again (Flush King), and now open Valve B (Black tank) and watch the magic!
You'll see a LOT more "stuff" come flowing out! A lot!
Once the water and stuff from the black tank stops again, close off the Flush King (Valve A) again, and open Valve C (gray tank) again and let it flush backwards into the black tank (again). Wait 10 seconds and then close off Valve C (gray tank), and open Valve A (Flush King) again and watch the second round of magic! OMG! How much more comes out the second time! YOU WILL BE AMAZED! Who would think you'd get so excited over watching POO! But I bet you will!
OK, repeat this procedure 1 more time. Each time you back flush the black from the gray tank, the water level in the gray is getting less and less of course. You do want to try to keep a bit in the gray after the 3rd back flush.
After the third, THEN close off Valve B (Black tank), open A (Flush King) and C (Gray tank) to clean out the sewer hose.
This entire process does not take very long. And I think once you've done it, you'll do it EVERY time you dump for ever more! Your black tank will never smell and will always be flushed out. You'll never have build up, and you really do not need to wait to dump your black tank if it's not 100% full, like so many recommend. Just make sure you have a lot of water in your gray tank.
Now, when does the garden hose come in handy?
For those times you don't have enough water in the gray tank to back flush, or if you simply want to reverse fill either tank, or if you flush your black tank and don't have gray water to clean out your sewer hose, you can run the water from the garden hose through the Flush King to clean out the sewer hose. (close both black and gray tank valves if you want to wash down the sewer hose only.
I have only tried using the garden hose 1 time in over 15 years of having a reverse flusher. I see no need for the garden hose attachment. The back flush works quite well, don't need the garden hose.
As one final step, for example if you are winterizing and want to make sure your tanks are about as clean as they can get, after all the back flushing steps, fill your black tank via the toilet. Let it fill naturally, completely full, until it comes up int he bowl of the toilet. Then flush the black. I do this as a last final step before winterizing. Drain the black tank completely until it drips no more. Then you are ready for the pink-stuff for winter.
I hope this help, and hope it makes sense. Like I said, after you've done this the first time, you'll see how easy it really is, and how effective it is also. You won't do it any other way going forward.