Flash won't let me click "Allow" to share my webcam.

On rare occasions Flash wont allow the user to click "Allow" when attempting to share a webcam in Firefox.

In such cases, you can click in the "Adobe Flash Player Settings" dialog window to give it focus, then hit TAB twice to navigate to the 'Allow' button, and then press Enter.

This essentially uses the keyboard equivalents to click the 'Allow' button. The following animated GIF shows us using the keyboard to click 'Allow'.