What kernel version are you running? What webcam and driver? What mic and sound driver? What flash version?
While Linux development has been slower than Windows for many Windows-based multimedia content, Linux has advanced much throughout the years and is continuing to develop at a fast rate. Vendors are slower to develop in Linux, generally, but many more are supporting Linux. For what I have needed, I have not had many problems with Flash support in Linux. A while back, it did not seem to work very well, but it is much better now. Try to upgrade your Linux version or distribution, and install the latest Flash.