In Adobe CS5 you can export games to iOS, but all my research in the past indicated that Apple was not going to support Flash. It's my understanding that Adobe and Apple were working on this at one point and then Apple terminated the project. I was chatting with some other developers about this and one mentioned they were porting an AS3 project to their iPhone. Is there a way to get a Flash App on to the iStore? I don't think so.
Apple changed their mind about Flash-derived apps (as seen here). Developers can use Adobe's Packager for iPhone to convert Flash apps to native iPhone apps. The Flash VM is still not supported in the iPhone's browser.
You can't take a flash app and just have it run on an iOS device as-is. CS5 does have an export process to put projects on a device. I'm assuming it's running in a VM or is some kind of cross compiler or something.
Flash CS5 can allows you to export your flash app as a native iPhone app, using the AIR for iOS extension. But in order to create a native iOS app, you need the digital certificate from Apple, which you'll be given only when you register yourself as an Apple developer.