The external display and the camera might be using different refresh rates. If you're using a projector, you may also have an option to switch between different refresh rates in your computer's display settings.
For Mac users this setting is in System Preferences, then Displays.
If you don't have the option to change your display settings in Windows and you're using the AMCap software, you can go to Video Capture Filter from the Options menu in the camera viewing software. You should see some options to switch between different refresh rates (sometimes labelled as Flicker settings) on the right of the window. Please note that if you have a smartboard which is streaming the camera through its own software, you'll need to close that first in order to be able to select the camera and amend its settings.
If the flicker settings are unavailable, the system may be streaming the video in MJPG format which blocks the extra controls. To check, go to Video Capture Pin in the Options menu and locate the Color Space/Compression dropdown. If you change that to YUY2 mode, the flip/mirror boxes should start working in Video Capture Filter and allow you to tune the image.
In a few cases, visual flickering or flashing can be caused by choosing a video resolution too high for your monitor. You can change to a lower resolution in Video Capture Pin in the Options menu.