The Facebook credentials are stored in a cookie, so if the implementation of a logout method simply consists of clearing cookies.
If your app targets Windows Phone 8, there is a new simple API for doing that: ClearCookiesAsync.
Sample code:
await new WebBrowser().ClearCookiesAsync();
Here is a tutorial that makes use of it: http://www.developer.nokia.com/Community/Wiki/Integrate_Facebook_to_Your_Windows_Phone_Application