"The Paradise Hat" was never filmed,
Some have suggested that the story may have served as an uncredited inspiration for Harry Nilsson's The Point!. The Point! was produced by Nilsson House Productions soon after the rights to Vonnegut's story were purchased.
But the purchase of the rights to "The Paradise Hat" and the development of The Point! are discussed in Alyn Shipton's biography of Nilsson, Nilsson: The Life of a Singer-Songwriter and, other than the timing, no connection is made between the two stories.
If Vonnegut's story did provide some inspiration for The Point! it would have been advantageous for the producers of the film (and for ABC which aired it) to publicize the connection. In any case, it is unlikely that the album and film could have been released without a proper credit if Vonnegut was involved.