I am using MGTwitterEngine oAuth and LinkedIn iOS SDK in my iOS application with facebook-ios-sdk
TwitterEngine : https://github.com/bengottlieb/Twitter-OAuth-iPhone
'duplicate symbol' means one of your classes is #import'ing something twice that it shouldn't. If you look carefully, libLinkedInClientLibrary and libOAuth both symbolicate the same method '_EstimateBas64EncodedDataSize'. Check your #imports.
#import
libLinkedInClientLibrary
libOAuth