On windows, when you start the Fatpaint Flash editor, it will try to load our Java applet. This applet is not visible and is only used for some background tasks that Flash can't handle so well. It provides a better experience using the editor and makes the editor more fail safe.
When the editor is using Java, there are 2 systems to handle the saving of images. Sometimes Java will fail and Flash will take over. So this provides 2 mechanisms for saving images, and a much smaller chance that you won't be able to save your images because of a problem. When Java is not used, a separate Flash component will be used, but it won't have a fail over if the saving of images fail and you may loose your work.
Bottom line, allow the editor to make use of Java. If there is problems with it, install the newest Java plugin.