Using Rules module to Auto Post the content to Linkedin Account
Have you tried the LinkedIn Module?


  This module provides integration with the LinkedIn API. At the moment
  it supports the following features:
  
  
  Per-user OAuth authentication between LinkedIn and Drupal Post
  LinkedIn status from node edit form (like the Twitter module)
  Synchronise LinkedIn user profiles with a user profile tab in Drupal
  


For Drupal 7 it's still dev and there may or may not be any updates coming. But it would be a good place to start.