My FF portable won't play them on a remote instance of a proxy server.

Here on the public library systems they give you remote instances of XP loaded afresh each time for security and there is a lot of crippling of features for the same reason. But Opera portable reports a dialog requesting proxy passwords and so do a few sites like my mobile phone company website! Not that they offer much more than advertising. Needless to say I don't have the passwords, but I do have the evidence of the proxy server.

This is a fairly recent thing, FF2 (not the portable) on a memory stick can play Flash on the library terminals. (After it had been installed), so it is a FF issue (and Opera too).

Maybe your ISP has had something in place that only now is in conflict with FF.