ChatGPT explains it best
“Burning rage” typically refers to an intense, overwhelming feeling of anger or fury. It’s a metaphor that compares the emotion to something physically destructive, like fire. When someone experiences burning rage, they might feel as though their anger is consuming them, making them highly agitated, impulsive, or uncontrollable. The phrase is often used to describe moments where someone’s emotions are so strong that they can’t easily be restrained or processed in a calm manner.
It can also be used to convey a sense of injustice or frustration, like a simmering resentment that eventually bursts into an outpouring of intense emotion. This “burning” aspect highlights the destructive potential of unchecked anger.