I'm not sure, but I think not. To send this kind of information over the Net for each page - it would be a huge overhead. This info, when I collected it with JavaScript couple of years ago, was few MB of text. Even if encoded somehow, would be too big.
If you want it automated, you can write a redirection page, where JavaScript will detect Flash and do proper redirections.
I'm absolutely positive that Netscape provides such info (I think in window object, but may be in document). Not sure about IE, though.
And, of course, always provide links for those without JavaScript.