It appears that you will need to purchase a proprietary library in order to able to do this, as Java itself doesn't allow access to COM. Another similar question (about just Flash in Java) can be found here and a couple commercial solutions were listed.
I should note that whatever route you end up taking, you should optimally try to find a library that provides access to an Internet Explorer control, as opposed to just Flash or Adobe Reader. That's because, once you have access to an IE element, you can provide it with a URL (even if it's a local file) of either a .swf or .pdf document, and it will automatically load the correct plugin for each (I used this shortcut once for a personal C++ project in which I needed to load several different ActiveX controls). It appears that the EasyJCom library at the above link does provide such access to an embedded IE control.