Chrome now requires that all content accessing the camera or microphone be served over HTTPS.
Since Chrome mediates Flash Player’s access to the camera and microphone, you must authorize access in Chrome’s UI before Flash can see it. If the content is not served over HTTPS, then Chrome does not show the permission dialog, and Flash Player cannot access that hardware.
In order for the webcam service to continue to work in Chrome, the content provider will need to update their site to use HTTPS everywhere. The goal is for Chrome to force your content provider to protect your privacy, by ensuring that all camera/mic streams are encrypted when traversing the internet. (Without encryption, anyone with the ability to see traffic as it traverses the Internet can watch your stream.)
The best course of action would be to complain to your content provider and refrain from using their service until they provide a secure solution.
Alternatively, you could use any other major browser, as they don’t impose this restriction. As browser vendors do tend to roll out these kinds of changes in tandem, this approach may not work indefinitely.