How do I export iMovie 10 to .flv format?

You will need a file converter, for example this one:

http://www.iskysoft.us/lp/video-converter-ultimate/bing.html?=vc&utm_source=bing &utm_medium=cpc&utm_campaign=ISVC_SS_pid(1326)_UK&utm_term=convert%20to%20%2Bflv %20%2Bmac&utm_content=Mac%3A%20%20flv

It seems there is no .flv exporting option available in iMovie, you need to convert your iMovie project.

You may export the project to a .mov file via Share --> File and then convert to a .flv format.,

See at: http://www.digiber.com/convert/mov-to-flv-mac-pc.html