One option is to check if a Flickr URL is used in the item's media data and if so, reset the relevant OG image tag.
See how to override or add any meta tag here (as an example):
www.joomlaworks.net/forum/k2-en/51293-og-image-width-and-height#173709
A better option is to create a K2 plugin that dynamically swaps all $item->image or $this->item->image instances with the Flickr image URL. This will essentially have everything else work just as they do already with uploaded images in K2 items, across component AND module views.