The blues singer and guitarist Guitar Slim Jr., the son of Eddie “Guitar Slim” Jones, has been a New Orleans mainstay for years, though lesser known.

That’s about to change. We sat down at The Marsh Hotel to talk about where he came from and where he’s going.

Though there may be some special guests for his Jazz Fest set, what he guaranteed is, “I just get up there and do me. I had played 1...