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]
(..) I'll catch you later. Bye-bye, Donna. Good-bye. Dad, is the engine on fire? lt smells like something's burning. Something is burning! It's the engine! You stole the corn! I had it canned... over the store! (..)1992 Twin Peaks: Fire Walk with Me