Fooly Cooly is Tokyo slang for feeling somebody up, though thats about 14 years old now, so maybe its not used anymore.

I stopped by a Synch Point/Furi Kuri panel at Fanime con this year. I don't remember exactly who was there, but some of the guest were from Gainax... ok, after some research, looks like:

Yamaga Hiroyuki - Co-Producer (Founder GAINAX)
Tsurumaki Kazuya - Director
Sadamoto Yoshiyuki - Character Designer
Sato Hiroki - script writer
Takeda Yasuhiro - Founder/General Manager GAINAX

Also present were English VA:
Kari Wahlgren - Haruko Haruhara
Jennifer Sekiguchi - Mamimi Samejima

I do remember them talking about what FLCL/FuriKuri meant. They said that it had no meaning. They wanted to have a cool title, and they though it would be cool to have something that could be an acronym (like K.O.R. for Kumagure Orange Road). They made up some 'acronym,' but did not base it off anything. It does not have any meaning beyond that..