It depends on the context. In American English, a "burn" is what young people refer to as an insult. So it could mean, "I could accept my friends making fun of me". In an other context, it could mean the feeling you get from exercising. In any case, it means that you are able to endure something.

It can have a very perverse meaning, so I advise against using it. "The burn" means a feeling of pain or discomfort.

Probably it means "I can go through the fire".