Legend has it that this photo, taken at Gilmore Stadium in the late 30's was the origin of flamed paint jobs on Hot Rods. This is Fred Friday, a fuel leak on the exhaust started the show and he drove it to a stop without injury. Those Old Timers had some brass balls.
You are right. Those guys were tough. But, here's Don Prudhomme going through the traps at 200 MPH, wheels up AND on fire. He didn't lift until he crossed the line! And, as far as the origin of flames on paint? Nobody will ever have the answer to that one...that one will never be solved.
For more history and profiles of current flame painters see Up in Flames by Tim Phelps and Sam Radoff published by Motorbooks.
I think it was StreetRodder magazine that did a History of.... According to the article, the early flames were actually what we now call scallops, similar to the SoCal cars present red/white scheme, and were found mainly on El Mirage, Muroc, and Bonneville cars of the late 30's or early 40's. Variations soon came with longer points, then wavy "scallops". What we call traditional flames came along much later.
My guess is that there were probably some before the war, but the nose art and the actual flaming planes going down in the war probably inspired flames as we know them. I first saw them in Detroit, by Paul Hatton, in 1956. I know these weren't the first, but there were the best that I had ever seen in person or in the magazines. Blended enamel on black lacquer and striped.