Before you're able to use your microphone and camera inputs in your browser, you need to explicitly allow it in the Flash Settings window. That, however, can turn out to be easier said than done, but I'll explain a workaround.
Open your browser, go to any page with Flash content. Right click on Flash content and select Settings from the menu. A small dialogue window will open, with tabs at the bottom. Click on the middle tab (third from left) which depicts a folder and a green arrow. Now, click on the 'Allow' option, with the green check icon. Finally, click Close button.
This won't work, if, after selecting 'Settings' from the drop-down menu Flash refuses to accept mouse clicks. Basically, you can't do anything else in that dialogue but stare at it. If that happens to you, here's what you can do. Log out from your account, then log in to Unity 2D. Do the same process under Unity 2D, then log out and log back in to Unity 3D.