So... this is strange - I live edited the facebook posts and they have pulled in an image from the website icon NOT the featured image. The LinkedIn posts are still not finding any image.
Inspecting the page shows that the the server is returning a series of 404s for image tags????
My apologies, I just noticed that I misread your original query. The debugging tools are for blog posts, website pages, landing pages, not social media posts.
Sometimes you need to debug the post, LinkedIn and Facebook will then check whether there is new og information (such as the og image) and refresh the information. Simply insert the link and click "Debug".