You can easily add the "Login with LinkedIn" button to different areas of your site, including the JomSocial home page. Once added, users can login with LinkedIn, Facebook (using JomSocial or JFBConnect), or standard Joomla registration. There are multiple ways to add the LinkedIn login button. For JomSocial's homepage, you'd likely want to make a small edit to their template file to add our button tag, {JLinkedLogin}. Wherever you add that tag, the button will appear.
If you subscribe and need assistance, we can gladly help guide you through the process.
Hope that helps,
Alex