。
She was burning with anger.
Literal
She [topic-は] anger [to-に] burning was.
怒りに燃える is a metaphorical expression: 燃える ('to burn') applied to emotion rather than fire. The に particle marks 怒り as the cause or content of the burning. Japanese shares this fire-anger metaphor with English ('burning with rage'), but the Japanese phrasing — with the emotion marked by に rather than 'with' — is structurally different. ~ていた captures the ongoing state.