I want to integrate flash in my iPhone application so is it possible to integrate?
There is an application called Packager for iPhone from Adobe, which can be used to make iPhone app from Flash. I never used it though, but I think you should give it a try.
You can write apps in Flash that will run on the iPhone by using the Packager for iPhone. It only works with Flash and not Flash Builder. Adobe just released a revision after Apple changed its SDK license again so that it can run. Note that to run on the iPhone your app has to be compiled by Flash to a native iPhone app. You can't run just any SWF.
Also yesterday Adobe announced AIR 2.5 which claims to let you program for one runtime (AIR) and target multiple platforms including iPhone and iPad. The release notes explain that they will be updating their Packager to work with AIR 2.5 for feature parity with AIR 2.5 for Android.
No.
Adobe Packager appears to only be able to create entire apps, not library code that will integrate inside a larger app. There also is no complete Flash interpreter in a form that you might be able to bundle with your app (although there appear to be a few open source projects that claim to run a limited subset of Flash). Thus there is no way to integrate Flash into a larger iPhone application that will run offline.
Online, you might be able to run a Flash application remotely on a server, and serve the graphic results to an iPhone app using something like the VNC protocol.