"Hates his job, as Tinker thinks? "You have nothing to lose but your chains"? I am not convinced. More probably it's the chains of his family life, and of his unsociable mental constitution.

Or does it just mean the rattle of the escalator chains, which used to be quite a noise?"

All three at the same time, I assume, plus whatever other chains the singer or the listener experiences. That's how imagery works in poems and songs.