This is not directly related to Java, but Adobe labs just announced a preview release of Alchemy, which lets C and C++ libraries run to support AS3 in the Flash player. A while back there was talk that something similar was in the works for getting Java code on the AVM2, which is why I figured I'd post about it here.
The link: http://labs.adobe.com/technologies/alchemy/
It will be interesting to see how this compares to JNI - it looks like you're not running truly native code, as there's still a significant speed penalty, but I imagine the performance is still better than for pure AS3. In any case, it does look a bit simpler than JNI, at least at a glance, so it may be worth keeping an eye on.
Edit: ah, so the internals of this are based on LLVM, which I believe we discussed here a little earlier. It would be fairly straightforward to add a Java source (or target, for that matter) to this if there was interest.