No, you do not need a passport to fly from Denver, Colorado to San Juan, Puerto Rico. Puerto Rico is a U.S. territory, so travel between the mainland U.S. and Puerto Rico does not require a passport for U.S. citizens.
Do I need a passport to fly from Denver, Colorado to Kingston, Jamaica?
Yes, you do need a passport to fly from Denver, Colorado to Kingston, Jamaica. Jamaica is a foreign country, so travel between the U.S. and Jamaica requires a passport for U.S. citizens.