This will take a little experimentation to solve.  Firstly boost lighting with a halogen desklamp. Note that fluorescent (old style bar) lights are prone to flicker, the new compact globes should be fine. If you can light with those energy saving fluorescent lights that can help.

Camera settings can be adjusted.  Go to the Settings > Capture settings menu item.  You should see your webcam details appear.  Click on the format button.  What you see here depends on your webcam.  There is likely to be an option to change the frequency to either 50 or 60 cycles.  Try changing this setting.  Try different adjusting exposure settings here, and click "Apply" to see the changes on the video.  There is usually a "Default" button that will take you back to the standard settings.

Usually, more light from even lighting sources solves this issue.  Tungsten globes and old style fluorescent lights will flicker somewhat.