Ok based on your comments from the answer above I get a sense that what you are trying to do is invoke a swing window INSIDE your LibGDX game window, which is an open GL rendering scene.
Let me stop you right there. The swing toolkit invokes its own rendering engine, because it's not intended for this purpose at all - it's intended for desktop applications. So when you instantiate the dialogue, all sorts of other oracle java stuff gets instantiated along with it, like the Graphics2D class. You can't just add this class to a scene2D stage and expect that it draws. They don't implement the same interfaces or inherit from the same base classes. The draw(Graphics2D graphics) method that your JFileChooser implements is not the same as whatever draw(SomeClass foo) method that your libGDX classes implement.
So if you want to make a file chooser window, you need to start looking at the libGDX widget libraries. There might be something that someone has put together already, but my approach for my next libGDX project is going to be to extend these classes for my own UI libraries. I don't know what your project is, or what your timeline is like, but it's certainly a better approach then trying to adapt the swing toolkit to render in an OpenGL rendering scene.
edit
After some quick reading, I'm going to go one further and hazard a guess that the way the swing toolkit gets rendered is entirely dependent on the implementation of the JVM for a specific platform. Now this is where my CS knowledge starts to be a little limited, but I would hazard another guess that this is way way different than the LWJGL implementation of OpenGl by way of using Java wrappers for C libraries.