the flames doesn't have to be on his back.
king has to manually place the flames in the areas he wants to protect.
he coated his wings vs tatsumaki/the half of his face vs shishi sonson
simply put: king can't use his flames at all when he enters speed mode.
but when his flames are out he loses the speed bonus and gains durability.
that's why he wasn't able to dodge zoro's last attack.
at the end of the fight he was using his flames on his hardened sword and used it to block zoro's attack, but failed.