Where can I find a list of Vietnam War casualties from the State of Florida that includes their branch of service?
The Vietnam Veterans Memorial Wall Page includes a search engine that will let you search by just about any criteria, including first name, last name, birthdate, and home of record.
The National Archive has complete statistics, although it takes a bit more digging to find them. Here's their complete list of U.S. Military Personnel from Florida Who Died as a result of the Vietnam conflict.
—The Fact Monster