Can you use the cavern of flame to remove a ready character from a story or only an exhausted character?

I'd say it works with ready characters, as well.

I agree with Jhaelen--the way it's phrased, the two effects resolve at the same time "Ready that character, and remove it from the story." Since there's no "If" or "then" thing going on, you just resolve as much of the effect as you can (removing the character from the story) and don't worry if you fail enacting the other bit (readying the character).

I would agree, they aren't dependent so you're good to go.