To build and generate your own Flash games for use on a J2EE application server, you would need to create the games using software tools like Adobe Animate (formerly Flash Professional). Once you've developed your Flash game, you can export it in the SWF format, which can then be integrated into your J2EE application. However, it's important to note that Adobe Flash has been officially discontinued and is not supported on most platforms. This may limit the viability of this approach in a modern context. Consider using more current technologies such as HTML5 and JavaScript for game development, which are more widely supported and compatible with modern web standards.