She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) Timon? Yeah? Pumbaa. I don't wonder; I know. Oh!...What are they? They're fireflies. Fireflies that uh, got stuck up on that big, bluish-black, thing. Oh. Gee. I always thought that they were balls of gas burning billions of miles away. Pumbaa, wit' you, everything's gas. Simba, what do you think? (..)1994 The Lion King