ChessMate Pocket Set
Bobby's pocket set from Pawn Sacrifice

I'm wondering if such a set was available in 1972. Didn't Fisher famously use, for analysis, a leather chess wallet he picked up long ago in Argentina? I believe that Larry Evans wrote that he also had one.

Yes, indeed. Chessmate is definitely the way to go. They are the only company to my knowledge producing contemporary pocket chess sets/ chess wallets. Aside from them , your best option would be buying a vintage soviet set. I contemplated purchasing the Chessmate Ultima , however, felt the price was a bit too steep for its lack of utility with the prevalence of chess apps on the phone/ tablet. Nonetheless, it's a very niche item reminiscent of the "glory days" and is a conversation piece.
Just watched Pawn Sacrifice. OK movie. Near the end they show Bobby leaving after he had won and he pulls out a magnetic pocket set that seems to be leather and has a zipper to close it. Does such a set exist?