I've worked on this for over two weeks. I cannot export with any setting to create a flash video. My Quicktime Conversion options are:

3G
AIFF
FLC
iPod
Apple TV
iPhone
Quicktime Movie
AU
AVI
Wave
DV Stream
Still Image
Image Sequence
iPhone (Cell)
MPEG-4

Did Apple have a spat with Adobe?! I've heard that FCP 4 had Flash listed. Do I now need to buy something more after getting CS3?

Not sure as I do not use final cut, but, as more people upgrade to the newer flash you will actually be able to use mpeg4 / h264 files which look better even at smaller file sizes. Hopefully another FCP user can help answer your question about the FLVs though.

Doing a quick google search it looks like you need to get the Episode Plugin in order to get access to the other formats.

http://www.telestream.net/products/episode_pro.htm

another stand alone option:
https://flix.on2.com/

My guess is apple did not want to pay for the royalties adn left that to the user?

$400. Dang.

So everyone who makes Flash videos is buying all this extra stuff?

If Final Cut 4 had it, how did they ever manage to sell FCS2?

I think FFMPEG X can also do flash, never used it too much thought but it is free. You just cannot do On2VP6 FLVs

$400. Dang.

So everyone who makes Flash videos is buying all this extra stuff?

If Final Cut 4 had it, how did they ever manage to sell FCS2?

Final Cut doesn't have Flash export capability unless you purchase the Flash upgrade. Been this way since FCP 4 or 4.5 when I started working with it.