Agree with the OP and while as per manga the flame is not shown, however, there are a few points:
a. So far King has only used fire based moves when he is Flame On Mode, why would it be different for the last attack?
b. King starts blocking Zoro's attacks while he is in Flame On Mode, if he is invincible in Flame On then why does he block or why run away when Zoro notices and comments on it?
c. Zoro understands that he can hurt King even in Flame On Mode so he goes for the all out attack, because just before King starts to block (after getting hit by Bird Dance) Zoro already pointed out that it is pointless to attack King in Flame On Mode
As for the people calling Sera's completely invincible, please check the official translation:
Zoro says "Your attacks won't do any damage unless the flames are out, they are basically invincible when the fire's on". Zoro didn't include himself or he would have said Our Attacks instead of Your Attacks.
Kid King had bandages on him when he was getting experimented upon in PH. The Seras are made from Kid King's DNA and even VP knows they are not fully invincible as he said that they have not been tested against lasers.
King >> Seras > Kaido in toughness