You're using the built-in debugging server, which does not handle concurrent requests. To use something standalone, that's a bit more robust, use uwsgi:

    zmusic-ng $ uwsgi --chdir backend/ -w zmusic:app --http-socket 0.0.0.0:5000

I've updated the README to reflect this suggestion:

http://git.zx2c4.com/zmusic-ng/about/#standalone