The schooling fish available in the hobby are relatively few and far between, mainly because many of them aren't terribly pretty. I did a lot of research on this (but no experience with any of these). What I've heard:
1. chromis or other damsels (including clownfish) - their nature is to school when they're small, but when they get to sexual maturity they establish territories and pair off. In the wild, they may or may not pick their own section of coral and still school part time, but in the confines of an aquarium they won't have enough territory and will kill each other. Thus the general story I've heard is that they're fine when small for like a year or so and then they pick each other off until only 1-2 are still around.
But this is not everyone's story; some folks have been luckier, not all chromis and damsels are alike, and based on the clownfish harem experience, if someone really wanted to try this, I'd recommend getting an a group of chrysipera clownfish from ORA, all from the same clutch (with a dominance hierarchy established) and put them in a large tank (say, 11 fish in at least a 48x16x21 75g) with lots of (fake or real) branching corals and places to hide.
2. firefish - won't do it, at least long term in aquarium conditions
3. cardinals - small banggai will; however they also pair off. Same goes for PJ cardinals. THAT SAID, Banggais will reportedly school with
blue streak cardinals, who supposedly will school. So if you had a school of say 5-7 blue streaks and a pair of banggais they supposedly will permanently school together.
4. all kinds of relatively obscure cardinals and gobies of the genus
Ostorinchus (school in either seagrass lagoons and/or cave areas), gobies of the genus Eviota (school among real or fake coral heads, branching SPS, and/or caves), or Coryphopterus (school in real or fake branching SPS, available sometimes
aquacultured or
sustainably collected in the USA by collectors with substantial investment in coral reef protection)
if one is really looking for schooling fish, I'd contact Kara or Phillip of KPaquatics and ask them if they know of any good schooling fish candidates that people don't think about (since they know fish very well, including things that aren't commonly in the market), and while you're at it if they could catch most/all of a school for you.