Kirk's line from TWOK. His other one when he cut short his inspection of the ship and mouthed the word "later" too: these sound like tag lines for ads in commercials or something. Were these jokes from the popular culture outside Trek at the time?
The first one, "a chance to get away from it all" is just an old expression. I don't remember it, or the other one being from any comercial or being a buzz phrase of the time.
I don't see how either of these things would have anything to do with pop culture. They're just expressions.
"Get away from it all" is an expression that's been around for many decades. It inspired a fanspeak term: "GAFIATE" (verb) - to Get Away From It All - to leave fandom, either temporarily or permanently. Somebody wrote a filk song about it (I can only remember the chorus).
Actually I do recall “This’ll be your big chance to get away from it all” being used in a TV commercial for an upcoming broadcast of the movie. Funny how it stuck with me all these years.
God knows McCoy needs to get away from it all throughout his lifetime. He always practically seems on the brink of a nervous breakdown. That guy deserves a vacation that doesn't get interrupted. Case in point: The Final Frontier, I mean, let the guy eat his beans and whiskey in peace before he completely snaps!