I'm confused. After rewatching The Flim-Flam Man, I looked online and on various online resources, they all mention a song for the film, called Flim-Flam Man and it has been covered by such as Barbra Streisand. But I know that the film doesn't have a song in it nor on FSM's CD. I haven't the disc to hand (it's at home), so I can't reread the liner notes at the moment.
The liner notes for the FSM release of THE FLIM-FLAM MAN by Jonathan Z. Kaplan don't mention a song, and I have never heard a song musically related to the movie.
The record is on 20th Century Fox (like the film) and came out in 1967 (like the film) but I don't see anything further that absolutely connects the two.
(Oops - edited to add, it looks like the Italian release does says it's "colonna sonora originale del film" --- ?)
The Laura Nyro song was titled "Hands Off The Man" (the song's first words) when her album "More Than a New Discovery" was released in 1967. When the album was re-released as "The First Songs" in 1969, the title of the song was changed to "Flim Flam Man" (the song's next and most repeated words).
In the "what might have been" column, a 2 September 1966 Daily Variety news item indicated that producer Lawrence Turman approached Bob Dylan to write the film’s title song, to be sung by The Mamas and the Papas; however, neither Dylan nor the group were involved in the final film.
Obviously, the song has nothing to do with Jerry Goldsmith and the connection to the movie THE FLIM-FLAM MAN seems to be a loose one at best. Perhaps the original idea was to have this or some other song involved in the film, but that idea was later dropped? Was it actually written for the film, as Wikipedia suggests (but which is terribly unreliable)?