I have the flush king also and like the way it works. I've never flushed the grey tank with it but that's not to say you can't or shouldn't. It won't hurt to do if you want. For sure the black tank though. Just make sure you open the black tank dump valve before you turn on the water, otherwise you will pressurize the pipe between the two valves and run the risk of a pipe rupture. I've seen it happen.
I watch the tank fill through the toilet and typically let the tank fill with water until it just starts to come up the pipe between the tank and the bottom of the toilet. Mine is a straight shot down so its easy to see when the tank is full. As soon as I see it's full I go out and shut the water off and pull the valve on the flush king. Works like a charm every time. Just don't get distracted and forget about the water being on. I know a guy that flushes his 140 gallon blank tank like this twice every time he dumps. Does he need to fill up all 140 gallons or do it twice? Likely not but he claims he's done it this way from day one and has never had any black tank odors and he uses no blank tank deodorants or chemicals of any kind.