Getting anonymous anything is getting harder these days. It really becomes a tangled web.
It really depends on what your ultimate goal towards anonymity is, are you trying to stop people from reading the contents of your mail? or tracking you down...
If is domestic spying your worried about, get an email abroad in a place that is not as likely to cooperate with the US, like China, or Pakistan, and have it forwarded to a middle man, a friendly nation less likely to raise flags, convoluted, but possible. The government is probably less interested in packets from Denmark, than...North Korea.
Still not truly anonymous. Public Wifi?, from a few blocks away with an Alfa? Of course you changed your MAC Address, and disguised your hardware flags and OS identifiers on your operating system. Not that it would matter, you're running a Live linux distro, with Full disk encryption of course, with a 64 char password...