I don’t know about Flatpak (it is a different project) but it is easy to build an AppImage from a jar. Essentially you bundle JRE and the application into the AppImage.
I don’t know if it is possible using Windows (possibly it is but I don’t have a Windows machine), so I think the easiest solution for you is to use a service like Travis CI or GitLab CI that builds the AppImage in the cloud.
Here are some examples of yml recipes for Java applications:
https://github.com/AppImage/AppImages/search?q=jar+ingredients&unscoped_q=jar+ingredients
You run these using the pkg2appimage command on a Debian/Ubuntu machine.
I am the new maintainer of a Java open source software.
Can you point me to your software? If it is living on GitHub or GitLab, I may even be able to send you a pull request/merge request that would build the AppImage for you.