Proxychains are working fine with iceweasel/firefox on TAILS if you want to first go through the local tor socks proxy and from there to a proxy of your choice to hide the fact that you are using a tor exit node, as might be necessary for some services. Just turn off the proxy usage in the browser and put the local tor socks proxy and the proxy of your choice into proxychains.conf, using strict_chain mode.
Since tor-browser brings advanced customization for security and anonymity over iceweasel/firefox, it would be desirable to use tor-browser instead of iceweasel.
In TAILS tor-browser is protected by AppArmor and the respective config is found in /etc/apparmor.d/. Since proxychains is hooking some networking syscalls in tor-browser, AppArmor seems to get in the way of proxychains:
Can't locate proxychains.conf: Permission denied
One can insert statemets in the AppArmor profile config to allow tor-browser to access the proxychains.conf file in its default locations. This does NOT solve the problem! Obviously there is something more that needs to be done about AppArmor. Alas, I do not have enough experience with AppArmor to find the right leverage what needs to be done to get proxychains to work with tor-browser in TAILS. Solutions are highly welcome.