She burned with the flames of jealousy.

Literal

She [topic-は] jealousy [of-の] flames [object-を] burned.

嫉妬の炎を燃やす (to burn the flames of jealousy) is a vivid metaphorical expression — jealousy as fire is a powerful image across cultures. 嫉妬 (しっと) is the formal word for jealousy. 炎を燃やす (to burn flames) makes the metaphor active: she's not just jealous, she's actively stoking that emotional fire. The kanji 嫉妬 uses two complex characters that learners often find challenging.