It's easy to prove it - post a single instance of Zoro cutting King a single time with his flames on his back on. Everytime he cut King it was with his flames turned off in his back.
Ok, are you agreeing or disagreeing with me lol.
I agree advanced armament Zoro can't damage King in flame on mode.
For for your panel, I think King was in his flame on mode when he was finally cut by KoH mode. Because King has always been in flame on mode while using fire.
But I agree it is unclear, since we can't see it all too clearly with all that flames overload.
Regardless, I would say it has also been pretty clearly implied that KoH advanced conqueror's Zoro can hurt flame on King. That was the entire point of the panel with King blocking, followed by Zoro's taunt of "why are you blocking now?"