At the end of the day, there has to be a legitimate reason for the Lunarians and the Seraphims to ever turn off their flame. If it's something that's not connected to a certain specfic condition, they could just choose to stay invincible for as long as they wish and therefore could not be defeated.
Zoro himself was wondering whether their wings are just decoration. Perhaps they need their flame to enlive/animate their wings, so "speed mode" isn't really "speed mode", but "flight mode", that simply boosts their speed noticeably. Might turn out to be that at the end of the day you can only kill those guys, if they are in a position, where they have to fly.
It's difficult to check this assumption tho, cause of King's different forms, i.e. base, zoan and hybrid. For base and hybrid King that assumption holds true, but Zoan King does both flying and gliding and the transition between those two is often difficult to depict, even if his actual "flight/acceleration" sequences get the "flap"-sfx.