Probably the last resort type answer before making your own browser :P (if all else fails) but you can install Easy Debian and then set the proxy in ice weasel (rebranded firefox).

You can also use firefox mobile and then navigate to "about:config" which will bring the firefox settings, then manually enter the proxy details (should be network.proxy.http etc, maybe set it on a desktop and then copy the same changes over). Only issue is I don;t know how to turn on the proxy in firefox... just set it Maybe I missed it somewhere in the settings.

EDIT: its under Network.Proxy.Type set it to 1 to enable the proxy.



BTW I haven't actually tried all this (as i don't know a working proxy at the moment) but it should work if its all there like the desktop version.