Current versions of Google Chrome now require that any content attempting to access the camera or microphone must be served over HTTPS. Google mediates access between Flash and the Camera, so we can't even see that a camera is available until you authorize it in Chrome. If the content isn't served over HTTPS, Chrome will automatically block the camera/mic request, you won't get an authorization dialog, and Flash will never see the attempt to use the camera, nor will it be able to access one.
Chrome's goal here is to force content providers to protect your privacy, by making sure that all camera/mic streams are encrypted. The content provider will need to update their service.
As a workaround, you can use a different browser.