Yeah so King defense increase when King is using his flame. And during the Tatsumaki he is using his flame to cover himself and boosting his durability.
Just after the Tatsumaki King is saying this : he clearly talked about his Lunarian gimmick. And there is no healing. Just protection.
Zoro cutting King without him using flames to protect himself:
There are no flames stopping Zoro's slash here^^
King going white-eyed implying the attack cut him and flames appeared in the damaged area^^. King's completely fine in the panel right next to it. He blow himself up and remained completely harmless. Zoro cut him with Onigiri and the cut completely disappeared. It's pretty clear King can heal his ass with flames.
Also, the flames weren't covering his wings during Tatsumaki
He had flames behind him, but it wasn't covering his entire body. Zoro also literally says he's blocking with wings.