They are not down. Its just the same old bugs. In the past you would often end up in an endless redirection loop (redirecting between countries), having a "Too many redirects" error as a result. Their website just sucks.

This specific error posted above I got as well recently. Solution is, like with any KLM/AF website issues, clear the cookies for that website. I'd advise against clearing all your cookies, but through the settings of your browser you can typically do so for a specific website. After having done that the site works normally again. Its absolutely ridiculous that this is needed to get access, but unfortunately these issues have been going on for literally years - and nothing is being done to resolve them. These issues are especially apparent when you are logging in from abroad, or are visiting a specific-country website other than the country that you are currently in.