When SWF/FLV files on the web page are not displayed in “Download online Flash movies” window, however, you can see Flash animation when browsing the same site with any browser, please, make sure that supplied URL, actually, has any embedded Flash resources.
It may happen that the main page (index.html) doesn’t have any Flash animation but only still images instead; however, the other pages that could be accessed from the main page by clicking links may have ones. For instance, http://some_web_address.com may not contain SWF/FLV files but http://some_web_address.com/swf.html has the ones.
One of the simplest ways to check whether the loaded page has embedded Flash animation is right-click Flash animation on the page and check if the last menu option is “About Adobe Flash Player“. Alternatively, you may check the HTML code of the loaded page for SWF/FLV file extension occurrence.