The concept of "Flutterbat" originated from fan art and fanfiction, not from the official show.
In these fan creations, Flutterbat is often depicted as a darker, more powerful version of Fluttershy, sometimes with a bat-like appearance or supernatural abilities. It's a popular trope in the fandom that explores the potential for Fluttershy's gentle nature to turn into something more assertive or even aggressive.
However, there's no official story or explanation for how Fluttershy becomes Flutterbat in the show itself. It's entirely a fan-made interpretation.