Create Linked Server to AlwaysOn Availability Group Listener
Finally found a tutorial here: http://www.derekseaman.com/2014/10/sql-2014-always-ag-pt-12-kerberos.html

The problem for me was that I needed to register the SPN for the Availability Group against the Managed Service accounts that are used to run the SQL Database Engine (step 8 in the link). Once I did that and restarted all 3 servers in the cluster everything works.