When Weasels become agitated, they immediately begin to do this. The general action is for the weasel to shake uncontrollably, turning back and forth, with eyes wide and mouth open, tongue sticking out. Weasels may use this as an attack or just to scare away people. Ogling, however, has an effect on their crazy blood-driven rage and calms them down.
Derivatives of Flipping the Fuck out are used exclusively by the Weasel King, one being "Pondering the Fuck out" when he is concerned about the ultimate fate of the universe. The most powerful flipping out, however, is the Weasel King's "Final Flip Out", wherein the aforementioned king fuses with Problem Sleuth (who is also using Sepulchritude) and the two combined deal massive damage, capable of eliminating the hundreds of health meters of Demonhead Mobster Kingpin in short order.
Nervous Broad also uses this move when she picks up her lipstick which causes her to NERVOUSLY FLIPS THE FUCK OUT
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Hysterical Dame uses this move when she picks up her teddy bear which causes her to FLIP THE FUCK OUT HYSTERICALLY.
In Homestuck, a player commands John to do this while he is attacking some imps. Similarly, as the first Ogres approach, a nearby imp quickly absconds the fuck out of there
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Lil Cal causes Dave to sort of flip the fuck out.
In the Midnight Crew Intermission, Clubs Deuce, after realizing that he is holding a Bull Penis Cane, proceeds to flip the fuck out.
Eridan flips his shit and kills Feferi and Kanaya, so Karkat flips the fuck out.
Jack Noir, with the power of the Black Queen's Ring, flips the fuck out legendarily on the Battlefield.
It isn't said directly that Doc Scratch flips the fuck out, but what he does is pretty similar.
Similarly Jadesprite pretty much flips the fuck out immediately on prototyping. As does Tavrisprite.
Sollux asks Aradia to calm her robot versions down because they're about to flip the fuck out.
In [S] Collide, Hussie flips the fuck out like a weasel while in Homosuck mode.