The complete story is told in the post entitled, "Runaways at Mullins Cove."
Minnie described Captain Frazier as old, wealthy, and kind. She also reported that he had sons who became well-known lawyers. He had house servants as well.
In light of Minnie's words, Captain S. J. A. Frazier fits the description.
S. J. A. Frazier was a former Confederate captain residing in Chattanooga at the time of the runaway story. Some details about his life may be reviewed at Chattanoogan.com.