How long can I wait with chest burning to see if it goes away without seeing a doctor?

Burning or pain... Most often "burning" is used to describe the sensation associated with acid reflux, in which case you should tell your doctor and they can guide you in how to deal with it. Occasionally, "angina" is described as burning, as opposed to chest pain/pressure, in which case you should approach this with some urgency. Tell your doctor about your symptoms, what brings it on, and what improves it, etc., .