You can read them independently, but I read them in order. I believe it helps especially to follow the St. Cyr "arc". OTOH, each one has a separate new storyline.
Hold it. There is a 7th one I didn't know had been released. The Day Ends At Dawn - apparently the last in the series. I'm getting it immediately. Love how he incorporates Buddy Bolden into the stories. St. Cyr is also a great detective character.