This is the demonstration of authentication against kerberos-enabled proxy with Java's Krb5LoginModule.
You need to have running kerberos authentication server. If you don't want to install your own Kerberos and just need something quick to try then you can use demo freeIPA server.
You need to have a proxy with kerberos authentication in place.
One such proxy is Squid - see Proxy Authentication for more details
Update username and password in KerberosCallBackHandler
and proxy host and/port in KerberosAuthExample.
If appropriate, you can also update configuration in login.conf file.
Just run KerberosAuthExample main method.
If everything works, you should see content of example.com in console.
There's a great proxy-vole library which can be used for proxy configuration detection.
If you want, you can use it to detect system's proxy settings and use
system-wide proxy instead of hard-coded one in KerberosAuthExample - just
use appropriate proxy selector to retrieve proper proxy settings
// for java HTTP stuff
ProxySelector.setDefault(proxySearch.getProxySelector());
// for HTTP client, you have to set proper proxy router planner
...