Fortunately I noticed that the SWT browser allows you to listen for changes in the status text, so as a proof of concept I made a little project. Its nothing too exciting, but it shows how you communicate both ways and with a bit more work and some clever serialization I should be able to pass some rudimentary data types back and forth.
If you want to have a play you can download a zip file of the eclipse project here.
You’ll need to make sure the SWT library is on your build path to get it to compile. I’d be interested to hear if anyone has any problems using this, or if anyone makes any interesting additions to the code so we can do more complex java and flash communication within SWT.