Hello, Grant and Welcome to GreekChat.
There aren't many KA's on the board, so I thought I'd jump in with a few cents in case you don't get an answer right away.
In brief, I am aware that KA Order does initiate alums (my better half did so when an undergrad--his chapter initiated a faculty member that was recommended by the No. 1.)
However, the intricacies of how to go about it have never been explained to me directly.
If you're concerned about approaching a table in a public forum, you may want to address your question to the KA National site at
http://www.ka-order.org. There is a contact list of the national staff that can probably answer some basic questions.
Best of luck to you in your pursuit!
Adrienne