We were told clearly that King with his flames on can be harmed by Zoro once he attained ACoC in not one, not two but three situations.
- He initially acknowledges Zoro's new found power and the ability to hurt him and explicitly spells it out: "I can sense the threat you represent!"
- He then proceeds to dodge a CoC coated Rengoku Onigiri. This is a very drastic change in his fighting style considering that he barely dodged anything before Zoro attained CoC coating. Once again, proving that regardless of his flame durability, Zoro can now harm King badly.
- Zoro himself taunts King and asks him why is he blocking, parrying and dodging Zoro's attacks now.
- Furthermore when going for the final finisher, Zoro did not care whether King had his flames on or off. Because he knew that he has the AP required to cut King now.
At that point, King used his speed mode to try and land a few hits on Zoro to take him out - considering that Zoro's stamina is weakening since even with his flames, he would not be able to defend from Zoro's attacks. Once that failed, he immediately resorted to keeping a distance and attacking him with a long range Big Flaming Dragon. However, King does not know the fact that Zoro could cut fire - which led to the 103 Mercies Dragon Damnation finisher.
Just look at this in parallel with the Mr. 1 vs Zoro fight. Say, Mr.1 has a mode which reduces his durability but gives him speed and BoAT is Conquerors coating.
Once Zoro unlocks BoAT, Mr. 1 recognizes that and tries to harm Zoro with his speed mode. But that doesn't work and Zoro cuts through him regardless.
That's exactly what happened with King.