Meet Augie Jr., Coco Robicheaux, Mem Shannon and Brint Anderson, working New Orleans bluesmen.

At the end of James Brown’s classic R&B hit “Night Train,” he calls out the stops over the pumping horn section: “Miami, Florida, Atlanta, Georgia… Boston, Massachusetts, and don’t forget New Orleans, home of the blues!”

Some of this country’s most recognizable and unique blues people were born and raised in New Orleans; Snooks Eaglin, Earl King and...