I cannot stress this enough. It drives me crazy every time I see someone say this as I know that person is uninformed and is not working with these technologies because Flash DOES work on the iPhone and iPad.
You can create apps in Flash. They run very well. You do not need special software to run them. In fact, as a user you would never know your app was developed in Flash because you would get it in the app store. You probably even have iPhone or iPad apps on your device that were developed in Flash.
So where did this rumor come from? Flash does not work on the mobile browser. So people assume since it doesnt work on the browser it doesnt work on the device but that is very wrong.
Why would you develop an app in Flash instead of Xcode? Because that app can also run on Android. That means you develop one app that runs on both operating systems.