First off, I'd like to compliment you on how well your animation is.
Now onto the problem. To be honest, I did not see that much light flicker. I saw some, but it was pretty unnoticeable at times. If you still want help, I'll give some. Since LEGO are a reflective type of plastic, I'd suggest placing paper over your lamps. Just be sure your lamps don't get too hot. Next; don't point the lamps down directly at the LEGO- instead, point them at different angles. I point them up towards the ceiling of my room, and at the wall too. Every time you move your Minifigure, wait one second to let the camera adjust to the light change. Then take a picture. This way, the abrupt change in light from your arm casting a shadow over your set settles and goes back to normal. Next (well, you should do this before you animate at all), Is to make sure that all of your settings are on 'manual' and not 'automatic'. This gives you more control.
Now to move onward. It's a very good idea to animate at night, that way, there is no natural light coming from the sun which moves all day. But if you don't have the option of animating at night, place a blanket over your windows (or simply close the curtains). Then Turn off all appliances in your room which contain light (such as television, fish tank, etc.). Next, Make sure to wear dark clothing. Dark blue, and Black shirts work best, and if you have the option, wear a long sleeve shirt. This way, there is not a reflection off your skin from the light(s) onto your LEGO.
This is the advice i can give you, markus77, and I hope it helps you too, Penguinking.
- Mason