King saying he's near his limit is piss poor fan translation that's refuted by both raws and official release. These are official Viz scans:
Btw, there's also a panel of Zoro blitzing him in speed mode from get-go. The entire chapter was generic attacks or generic dodges or Zoro clowning on King. King failed to give Zoro any trouble.
Also, King got piss scared after being hit by a single named attack from Zoro and started blocking, that's it lol. Nothing says his flames got weaker- nothing implies that at all, just your headcanon stemming from a wrong translation.