Sometimes I wonder if he’s a manifestation of the sheer mystery of existence. Of it’s inscrutability. But I also like the notion that he’s soul of Arda, of the entire world itself. Like the concept of Gaia. Which has a male aspect and a female aspect in the couple of Tom and Goldberry.
Thats always been my take on his nature and origin as well, we know Bombadil can't be a higher heavenly power like Eru or even one of the Maia because its stated that he too would be eventually overcome and be destroyed should Evil win, which ties in with the Industrial themes of Sauron's brand of domination and how it is destructive to the natural world.
His whole vibe is very natural and Green-Man pagan deity - so it would make sense if he and Goldberry were physical avatars of the world itself like you say.
It would also make sense with the things he says about being in the world before the Dark Lord [meaning Morgoth] came to Arda, as the world was formed in the Song and then the Ainur [Maia and Valar] descended to it, so the only thing that would have been on Earth at that time... would have been the Earth itself.
But then again, as you say he may simply embody mystery and inscrutability itself - Tolkien firmly believed that his setting must have unexplained elements and mysteries.
Is it out of the question that Melkor knows about it and can use it if he wants? I’m not enough of a Tolkien lore nerd to know.
No, not a chance.
The Flame Imperishable is Melkor's entire motivation and reason for rebelling against Eru, the Flame is the very power of God himself - the power of true Creation, the ability to make something from nothing.
This power belongs to Eru and Eru alone, that is why Gandalf describes himself as a "
Servant of the Secret Fire" for the Fire and Eru are One, as an unfallen Istari he is a faithful servant of Eru's greater purpose and weilds his authority - a fact made clear when Eru himself returns him to Middle Earth as Gandalf the White.
With it Melkor would be able to create his own new universe and rule over it absolutely as Eru does over Arda, but because he cannot wield it he resorts to distorting other creatures into his servants and his image - hence why he makes the Orcs from warping the Elves, Werewolves from infusing wolves with evil spirits and his own power etc.
The fact that these creatures are not truly "his" creations is also why Melkor is consumed by nihilistic rage and destructive pettiness, he wishes to destroy everything that doesnt come from himself and so once he is done corrupting and despoiling Arda and all of Eru's works he would then destroy them until there is nothing left.
Making The Secret Fire just a generic term for magic, or just a form of magic others can use, is directly detrimental to the entire mythology/cosmology and spirituality of Tolkien's work... which considering the mythology and spirituality of the setting were by far the most important aspects to Tolkien himself as a reflection of his own belief system, is quite unforgiveable.