Hi, I think a plugin isn't the better solution, in fact a plugin can check if the hosts is up or, for HTTP, if the page is an error page. It can't check for example if the domain is expired. However there aren't plugins like this for Flatpress.
Making a plugin of a cURL would be good, altho some kind of database would be needed so the links wont be "spammed" with request's every time the page with the links are loaded. That's just a courtesy tho.