This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Matt, Note that none of the 508 tools care if you are using Java. They do care if your app is web based, so I'll assume you meant "to test a non web based application."
Our team only develops web based apps. However, we do have a manual checklist (which looks a lot like the paragraphs in the law) to manual verify anything that the tool can't test. For example, our web app provides PDFs for download. We need to make sure that those are readable by hand. I looked around for a tool for that a while back and didn't find anything.
I suspect part of the reason is that some people think Section 508 is for websites, when it is really for any IT resource.