“Goosebumps walkaway is the line that the guy says to the girl in the movie that gives her goosebumps and then he walks away forever,”
Nick is having a hard time saying goodbye to Reagan, too, and keeps saying the wrong things to her, so he devises a plan to act out a goosebumps walkaway to up his cool.
The "goosebumps walkaway" is the moment a man says something to a woman before he walks away, something so deep that the woman in question gets little goosebumps on her arms.
"He hit me with that goosebumps walkaway"