I think you will need some Server Side Magic to get this to work. Flash can load data via XML (which is the preffered way, but quite heavy), or by loading in Key/Value pairs (ie: key1=value1&key2=value2) via LoadVars. Looking at the deviantart page, there doesn’t appear to be an XML feed, so you may need to create your own.
Personally, I would host a webservices script on my webserver which Flash would call via XML.load() - the service would be called something like services/getRandomDeviant.
The script would then scrape the HTML of the DeviantArt page, find the JPEG image location (and any other details you want) and create an output XML file (literally output it to the screen).
Flash would then load this data as part of the load call.