It may also refer to two separate cultural figures:
In Shakespeare's King Lear (IV, i (1605)), he is one of the five fiends Edgar (in the posture of a beggar, 'poor Tom') claimed was possessing him. Shakespeare got the name from Samuel Harsnett's Declaration of Egregious Popish Impostures (1603), where one reads of 40 fiends, which Jesuits cast out and among which was Fliberdigibbet, a name that had been previously used by Latimer and others for a mischievous gossip. Elsewhere the name is apparently a synonym for Puck.
Jim Copp and Ed Brown have an album of songs and stories for children titled Flibbertigibbets On Parade.
When announcing her support for Hillary Clinton during the Democratic Party (United States) presidential primaries, 2008, the word was used by Elizabeth Taylor to describe what Hillary Clinton was "not". Meg Ryan's character, Angelica Graynamore said in "Joe vs. The Volcano" (1990)," I am completely untrustworthy... I'm a flibbertigibbet."
On the ABC television series Pushing Daisies the character Olive Snook is sent to a convent resembling the one in The Sound of Music. When describing her inability to fit in she says: "Nuns aren't my people, unless you're telling me flibbertigibbet is a title of respect."