Usually it's used in restaurants now when the kitchen is out of something. Instead of yelling out "we're outa salmon" you pass along "86 salmon."

As the guy above you said. Its old old organized crime lingo (as in Prohibition era). The mob always used to use code words for shit so they could claim innocence of crimes. I'm only familiar with it because I used to read lots of mob related fiction.

I heard it around T_D back on reddit some time ago. It was a hashtag they started, that failed to get any traction because the Left can't Meme.

Yeah, to "86" something is fairly old.