The band backing Buddy & Stacy in the film is Little Richards backing band the Royal Company. This was confirmed by Buddy Travis, Buddy & Stacy had been booked to appear at the show and since they were touring with Little Richard they asked his band to help out.
In order to sort out who actually plays in the band here are screen captures of the players made from the "Shotgun" footage. I'm hoping someone will be able to identify the (rest of the) musicians.
Front: vocals - Stacy (left) & Buddy (right)
Background: guitar1 - Jimi, bass - Johnny Franklyn 1 and 2 (correct spelling?), guitar2 - Glen Willings 1
guitar2 - Glen Willings, sax1 - unknown
drums-Harold? (surname?) 1
sax1 - unknown, sax2 - unknown
Far right: trombone - unknown
(unfortunately the trombone player is out of the frame for most
of the footage, this is the best shot of him that there is.
1 email from Buddy Travis October 2007: "The guitar # 2 is Glenn Willens, The Drummer is Harold I think, on bass is Johnny"
2 discussion at http://www.stevehoffman.tv/forums/archive/index.php/t-107450.html, Melvin Sparks had identified the bass player as "Johny Franklyn". The exact spelling of the bass players name remains a bit unclear.