Jeff, that term is older than the hills, not sure when I heard it first exactly. Perhaps it was around food that I first heard the term, not sure. My first job was working in my grandparent's Po-boy & delicatessen when I was 12. It was a family run business.
Interesting....I learned the term in the mid to late 80's when working as a waiter, we used to use the term "86 the special" whenever we ran out of the daily special. Anything we were out of....i.e. Done, Finished, etc. etc. Word was spread throughout the staff by saying it was 86'd....86 the green beans, 86 the redfish, etc. etc.
I once asked one of the Chef's the origin of the term but he didn't know, He asked an old guy he had worked with at the Rib Room in New Orleans who had been there forever, who wasn't sure either but thought maybe it had to do with whenever someone died....they would dig a whole 80 inches long and 6 feet deep. Hence, when your done, the term 86.
Actually found this LINK to an article about it's origins
...although it appears no one seems to be sure.