I am finished with the LinkedIN API module.
It's done and pushed to github.
It's now possible to add "Login with LinkedIn" button to the list of existing buttons.
Also when posting Question or Answer there is an option to also post to LinkedIn. The link to your Question or Answer will then be sent to LinkedIn and will be visible by people on your network on LinkedIn.
This is similar to "Sharing" on Twitter.
As with other social sites it's also possible to add LinkedIn to your existing account from the Viewing your profile page while logged in to site.
Also if you check the "Post to LInkedIn" checkbox on the "Ask" or "Answer" form and your account is not connected to LinkedIn, the small window will popup starting the "Connect to LinkedIn" process.
The new section [LINKEDIN] is added to the !config.ini.dist (which you rename to !config.ini)
Instructions on how to get your LinkedIn API key are in that section.