Metaphysical question - what do you suppose Tolkien meant to indicate by making the 'Flame Imperishable' so important in the early Valaquenta? It's supposed to technically be the thing that really drew Melkor off-course, is the stuff of souls, yet it winds up as this very mysterious, undefined force. Do you think it's the same light that filled the trees (and thus the Silmarils)? Tolkien loves his light, but I wonder how much these forces are connected in canon.
Oh my friend, you just ask the best questions. *evil cackle*
So, as for what the Flame Imperishable does, literally, that's pretty straightforward. (It's also sometimes called the Secret Fire, in case you wanted to search for that in an electronic version.) Eru uses it to kindle life in all beings from the Ainur to the Children, and without this force, that's impossible. Melkor goes searching for it and can't find it, and Aulë makes little dwarf puppets until Eru sparks them to life personally. Ye Olde classic subcreation examples, so on and so forth. Probably sounds familiar from our first thread ever!
I think that this theme of subcreation is really what Tolkien meant to hammer home with the Flame Imperishable, especially in the Ainulindalë. It's a force to give to living beings, not for them to control—and we never see it outside of this "life force" application. So, I don't really think that the Trees or the Silmarilli literally contained the Secret Fire, though I admit that would make a neat explanation for why Melkor was so obsessed with destroying the first and keeping the second.
But neither are we supposed to put the Flame Imperishable out of our minds when we think of these things. Remember how I mentioned searching for "secret fire" in an electronic copy? Well, I did! And the only time it's mentioned outside of the capitalized, proper force of Eru is in reference to... Fëanor.
...Fëanor grew swiftly, as if a secret fire were kindled within him. He was tall, and fair of face, and masterful, his eyes piercingly bright and his hair raven-dark; in the pursuit of all his purposes eager and steadfast... He became of all the Noldor, then or after, the most subtle in mind and the most skilled of hand.
And there's just too many connections here to dismiss, because when the man named Spirit of Fire grows to become a creator like there's a secret fire, the force of creation, inside of him? And he when makes three jewels with literal bits of his spirit, like a secret fire, inside? Isn't a coincidence. And notably, Tolkien says "as if," not "with," so this is still a simile—but it's a deliberate and telling one all the same.