Start typing your message, as usual. Then when you are ready to insert an image, press the image icon (
). A dialog box will pop up. Paste in your image URL, and viola !!!
Ok, if all you get is a broken image icon, then something is erroneous with the URL you copied. In fact, some sites (not sure about Flickr) will not let external sites (like this one) show an image.
(EDIT) The URL you copied from Flickr is for a web page, not an image.