I have developed such a library, and you can find it at github.com/jgh-/VideoCore
I am updating this answer because I have created a simplified iOS API that will allow you to easily setup a Camera/Mic RTMP session. You can find it at https://github.com/jgh-/VideoCore/blob/master/api/iOS/VCSimpleSession.h.
Additionally, VideoCore is now available in CocoaPods.