A "flame" is a slang word used as "boy friend" if you are a girl, or "girl friend" if you are a boy. An "old flame" means he used to be your boy friend, but not any more. If she was an "old flame" that could mean she was his girl friend for a long time, but not now. Any way, he lost her because she fell in love with another man. However, the man seems to deny that she was ever his girl friend. Maybe they were just platonic friends.... good friends but not romantic friends.