Disclaimer: this is my personal opinion and not a confirmed detail by Apple or Adobe but I believe that the iPhone WILL run Flash and Flash Video. The reason for my assumption is a TV ad for the iPhone which I just watched at apple.com.

The ad is called 'Watered down' and makes a point of the fact that the iPhone does not show a watered down version of the internet but the internet as it is with most of its features. It seems that in my book and in that of Apple this includes Flash - if the ad is showing an actual iPhone running the actual New york Times site, which includes Flash Video! Check this image which I grabbed from the ad.
The circled area holds a SWF including Flash Video and apparently it's rendering fine.








Compare that with this image from the Keynote by Steve Jobs which also showed the NY Times site but without the Flash piece...

I think this observation is extremely promising. Apple cannot seriously call its internet device NOT watered down without Flash support - or maybe they can?. And if it does support Flash then we all know what this means, for example live video and audio, amongst an arsenal of other features. Who knows, we'll know one way or the other soon.
Oh and by the way anyone claiming they don't want an iPhone is lying. And I don't want one either.