I have used Quicktime for Java, http://developer.apple.com/quicktime/qtjava/
, from Apple to play SWF files in JPanels. It works well though there is only support for Flash 5 (last time I checked) and it does not execute actionscript.
For storing information in the Flash file there are several ways you could do this:
1. Use Translate to add a simple gotoFrame() action in the first frame. That would effectively work as a bookmark allowing you to save the frame last viewed - however I am not sure how to get information on the current position in the movie from swf back to Java. I do not have the quicktime documentation available so the solution might be simple.
2. Store your parameters in the serial number (FSSerialNumber). This object can store strings of any length so it is easy to save information in a text friendly format such as Java properties or JSON.