“Flutter” has to do with “fleet” – quick movements as of things on waves or in air.

• 03.010 There were moths fluttering about,
• 05.033 Wingless flutters,
• 09.025 Bilbo was all in a flutter,
• 12.082 which merely fluttered aside
• 13.043 fluttering in the draughts.
• 14.019 something fluttered to his shoulder.
• 15.004 Then he fluttered his wings
• 15.013 Before long there was a fluttering of wings,

“flutter, v.” OED Online. Oxford University Press, June 2015. Web. 26 July 2015.