I've seen Amphisbaena alba and A. fuliginosa in South American zoos. I've also seen Trogonophis wiegmanni in Japan's Ueno Zoo. ZIMS suggests that these holdings are still correct. I vaguely remember seeing a post about A. fuliginosa coming to Europe but it was probably for private keepers (or a false memory).
While no US zoological facility currently holds amphisbaenians, I read that Jacksonville Zoo held Florida Worm Lizards in the past. Really a shame that this group has no representation in our countries zoos, or really anywhere outside South America.
ZTL doesn't list any species of worm lizards in captivity. ZTL collections have had 7 species of worm lizards, 1 species of Mediterranean worm lizard, 1 species of Cuban worm lizard, 2 species of two-legged worm lizards and 2 species of short-headed worm lizard I visited Frankfurt's Exotarium in 1985 and saw the enclosure of the Balsas worm lizard (Bipes canaliculatus) in 1985 but didn't see the animal
This may be rellevant to this thread. Wonders of Wildlife seems to have a pair at around October 2021. Weird Worm Wednesday | Ready for some ? Meet the worm lizard! This unique reptile is neither lizard nor snake. It belongs to its own family of... | By Wonders of Wildlife | Facebook
I know that a couple of labs have Bipes biporus and I think I saw something about one such lab successfully breeding them in captivity, but AFAIK, no zoos keep them.