A "flea's runway" refers to a hair parting, particularly one that runs central to the head. The fashion for greasy slicked down hair with a central parting has diminished and the term is not heard as much now as thirty years ago.
Linda was disappointed because George had not been to the hairdresser she had suggested. He still sported the long sideburns, greased down hair and flea's runway that she had complained of.
by Reg Acton October 15, 2006