How can I display a Flash4 image in a Java program?
The only Flash player written in Java that I've found is Java2D Flash Player. It's a work in progress as the author mentions but it's getting there. Since Flash 4 is a Vector graphics format you could write your own parser for it but that would be a lot of work (that's why there aren't more Vector graphics formats done in Java, i.e., svg, wmf, emf, flash, vml, pgml).
You could go to OpenSWF and look at the other flash players they have. An possibly attempt to use a player written in another language if needed. For now those are the only options that I've found.