This is a term used to tell people to subscribe to Flamingo the Roblox Youtuber. He used it in a video, but it got censored by the Roblox chat filter. He tried to make everybody say it.
A short-term relationship on which one does not wish to explain/elaborate/remember. Often used in a dismissive manner.
Girl #1: "Hey, what ever happened with you and Julian?"
Girl #2: "Oh, it was just a flingamajig."
Girl #1: "Too bad...Like my new shoes?" (or other change of subject)