What types of weapons or ammunition won't work with the Siren's Chain Reaction skill?

Orc JMR is pretty much correct; anything that isn't a gyrojet, rocket or e-tech gun will probably ricochet. Shotgun shot counts as "bullets" for the skill (and at least one pellet will almost always ricochet due to the amount of pellets). Elemental shots still ricochet.

Note that not all explosive elemental shots are "gyrojets", as mentioned in that question any explosive gun that shoots "bullets" can cause critical damage and can also ricochet. Torgue shotguns, pistols, some assault rifles and all spiniguns can ricochet. Rocket launchers, grenade launchers, and "torpedo" assault rifles all don't ricochet.

In testing I was unable to get e-tech projectiles to ricochet, which interestingly means that Gaige's Close Enough seems to use a different method of applying ricochet; best I can recall her skill DOES ricochet non-AOE e-tech bullets.

Note that it's never the "ammunition" that's the problem; it's the type of gun. All ammo types (except for Rocket Launcher ammo, because they're always explosives not bullets) can count as bullets, but not all subtypes of a certain gun always fire what counts as "bullets" (mostly due to e-tech and lobbed explosives/gyrojets).