Is Pensacola, FL the Second Oldest U.S. City?

No.

• Oldest continuously inhabited European-established city in the U.S.: St. Augustine, Florida – founded 1565 by Pedro Menéndez de Avilés (Spanish).
• Pensacola, Florida: Founded 1698 (Spanish presidio Santa María de Galve).
• Rank: Pensacola is the 7th oldest European settlement in the present-day U.S. (after St. Augustine, Santa Fe NM 1610, Jamestown VA 1607, Plymouth MA 1620, Albany NY 1614/1624, New York City 1624).

Pensacola's "City of Five Flags" history (Spain, France, Britain, Confederacy, USA) is distinguished, but it is not #2.