With chain-mail gloves, there's a decent chance you still have hands after the explosion.

Chainmail strikes me as more useful for kinetic than chemical protection.

E.g., when the experiment blows up in your hands (or near them).

I think the primary purpose is to keep the hot glass shards from shredding your skin. I'm guessing you wear standard rubber/plastic gloves underneath the chainmail to protect against the heat and chemicals.

I'm also curious. If the peroxide explodes, a layer of chain mail could protect against cuts from the shrapnel, I suppose?

I'm guessing, but since in other contexts metals are used as a catalyst to decompose HOOH I suspect that it protects your hands from direct exposure. This would release a lot of heat, but that's likely better for you.

isn't that the joke...? It wouldn't do anything to help but "Part of the purpose, I believe, was to make you think very carefully about what you were doing as you put them on"

Well, at least it keeps your hand in one piece for the surgeons to reattach.