Why do I feel my chest burning when I bench press?

Probably muscle ache. A burning feeling in your chest while you lift weights is most likely caused by working the muscle which in turn releases Lactic Acid and causes a burning sensation. Other less likely possibilities include acid reflux (brought on by laying down) or heart pain (angina). Typical angina would be more of a crushing, heavy feeling + nausea + sweating + shortness of breath - but it's not all typical.