How can gnome based applications such as rhythmbox use a proxy

Some of the newer GTK3 based gnome-applications ignore/don't use environment variables when dealing with proxies.

Instead, they use values stored in gsettings / dconf

If you use dconf-editor installed as part of the dconf-tools package you can define the proxy in a GUI manner.

First - set the proxy mode to manual as shown

Second - set the proxy host & port. If you dont have an anonymous proxy you need to set the authentication-password and authentication-user values

If your corporate network uses https then set the equivalent system - proxy - https tree values instead of system - proxy - http that is shown above.

Via the terminal you can use the following:

gsettings set org.gnome.system.proxy mode 'manual' 
gsettings set org.gnome.system.proxy.http host 'proxy.askubuntu.com'
gsettings set org.gnome.system.proxy.http port 8080
gsettings set org.gnome.system.proxy.http authentication-user '[host]\[username]'
gsettings set org.gnome.system.proxy.http authentication-password 'mypassword'

Where [host]\[username] corresponds to your corporate network credentials e.g. mywindowsdomain\fossfreedom

If your corporate network uses https then substitute http with https in the above terminal commands.