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]
(..) He was headed for destruction of property, but since it's your own property, I sweated him down to misdemeanor trash burning. The only thing is, it's not gonna be free. There's a grand fine, for towing and disposal, another grand (..)2011 TvShow: Breaking Bad Title: Problem Dog Season: 4 Episode 7
(..) into the mainland. I'll get a box of fuses. Brought you some candles. Ain't no big city fire trucks out here, so don't go burning down my house. ( Chuckling ) Man, that is some good shit. ( Humming ) Man, what the hell (..)2009 The Black Waters of Echo's Pond
(..) - You set the terms, you can change them. - All right. Ahhh! FRIDAY! The Vision? Boss, it's working. He's burning Ultron out of the 'net, he won't escape through there. You shut me out! You think I care? You take away my world, I take away yours. Whoa! What's this? Run! (..)2015 Avengers: Age of Ultron