OSX utility for copy/pasting a text file in a FIFO queue fashion
The closest I have seen to these requirements is Flycut (free on the App Store)

It's extremely simple to use, though it won't automatically pop an item off the stack then move to the next one.

However, when you invoke Flycut (assuming you are starting at the top of the stack), you can just press the down arrow key ↓ to go to the next item.  When you release, it pastes what is in queue.

So, your sequence of keystrokes would be:

First:  ⇧ Shift ⌘ Command V 

Second: ⇧ Shift ⌘ Command V then ↓

and so on...