If your camera has automatic settings, turn the auto-whatever off.

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Here's what I do. I always face my lamps away from my set when animating. It still provides enough light.I just don't have the lamps faced directly onto LEGO because LEGO are reflective. Then while I animate, I move the minifigure some, but here's the key part. Instead of directly hitting the capture button, I let everything sit for a second before capturing the frame. That way, it gives enough time for the camera lens to adjust to the light change from when my arm cast a shadow over the whole set.
Hope this helped some.
- Mason

I just undid the auto on the white balance and did a test and I got the light flicker to go away!
Thanks for your help guys!

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Lol what was my first reply? Already tried it?? Haha

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My one doesn't have white balance, yet I have the QCP9000.