On my Motorola Xoom tablet, when I accessed a web video chat site, adobe flash doesn't recognize built in camera (Front and Rear). I didn't get the familiar adobe flash player settings dialog that asks me if I want to allow the website to access my camera and microphone. Flash won't allow me to send video. But the camera worked fine with the camera app.
I tried snapping a photo within Facebook and also a video and the camera couldn't be found.
This is a Xoom issue. The camera on Xoom may not be working via web sites. Adobe responded that "Microphone and Camera API's are not currently supported on Android Platform." Developers plan to add support when they are able to access these devices through the browser API.