K2 already provides the necessary OpenGraph (and other) meta tags for social sharing. However LinkedIn may prefer to crawl your content first. Are you uploading the main item image via the K2 image tab?

If you used the K2 item image tab, you would benefit from such sharing features.

If this site's content is a migration from Joomla articles to K2, you can always use github.com/getk2/k2-iaki to grab the first image from your content and dynamically use it as a K2 image. Which should basically solve your issue with LinkedIn...