Yeah that's a very interesting topic. It's certainly strange that even Zoro with his CoC infused swordsmanship could not even damage flame mode King visibly, which in durability terms is surreal, even for OP standards. So It might make sense for arguing that flame mode simply means that they become invulnerable.
Recently I did deep dives into all kinds of Youtubers, that are all hella smart and creative: Parvision, Dak's Sake, Hidden Island, Randy Troy and such. And they talk a lot about the ancient kingdom, joyboy, the Sun God, the origin of DFs and such. And it gets more and more obvious that the Lunarians played a very important role in all of that and nearly everything ability related will ultimately will tie back to life force-/ soul energy, i.e. haki.
Perhaps the Lunarians aren't making use of fire per se, but the source is rather life force/soul energy, that just manifests into fire in the physical world, which they can then shape and transform to their wishes and even turn into magma, if they get emotional/they choose to.
With such a concept I might lean towards them being invincible in flame mode, but then it begs the question why it's this way and not the other way around, when they are seemingly "infused" with their flame in "flame off"-mode.
Maybe they work on that natural energy that is everywhere, that stuff Vegapunk was talking about. And they absorb it through a hole in their back, and the flame appears there, because it's the place where that energy transitions into their bodies and during that process it just takes on a physical form in the form of fire or heat.
And when their bodies are in absorbing state, they are just invulnerable, like some kind of indestructable or nearly indestructable containers. And when they use that energy, their bodies get "animated" and they are going from storage into action phase/mode. And that energy is perhaps, similar to natural chakra in Naruto, just the voice of all things, meaning the haki of the all surrounding nature or stuff like sunlight..?
Basically means: They are indestructable energy containers at base.
Or all of that and their bodies are just made of a substance that's very similar to rubber, that gets softer, when heat gets involved and therefore they get a drop in durability..?
But even though I like all of that, it's weird that King was bloodied by GB, seemingly before he was captured by his roots. Does it make them completely invulnerable to external damaging factors only, but can they still be crushed and internally damaged, what was also a major theme against BM and Kaido aswell? Or did GB just got the better out of him, when he was in speed mode?
That's a very interesting topic, bro. What do you think, especially about the GB bit.