I'm going to assume the calculations are being done in a Java applet in the same browser where the flash is running.
You can call Javascript from within the applet using the following code. This code could then update the values in the flash animation.
import netscape.javascript.JSObject;
JSObject win = JSObject.getWindow(applet);
win.eval("window.alert('Hello from Java')");
If my assumption is incorrect, then where is the Java application running? On the client or server?
If it's on the server then you need Flash remoting. I believe there are a few different Flash remoting techniques. Try searching for java flash remoting. You can make it call the server every 2 seconds or so to get the latest data.
If it's running on the client I doubt you can connect to it from Flash because of security. A signed Java applet could connect anywhere it wants to. You could retrieve the data using it, then push it into Flash using the method described above. Would be a crazy hack though. Can you do the same thing with Flex? (I've never used Flex before).