What is causing my frames to "flicker" after being rendered? I am having an issue in my renders where random frames are "flickering".  I am having the exact same issue this person was having and no one seemed to be able to answer his question: 
 What causes rendered frame &quot;flickering&quot;?

Here is my animation with the issue: https://www.youtube.com/watch?v=UcIcOf4g3-g

I have put hours into finding a solution and I can't seem to find one.  Here are the solutions that I tried:

I have tried rendering with motion blur OFF and it fixes SOME frames.  Still not a definitive solution though.

I have messed with camera settings.

I have rendered the shadows separately and the meshes separately.

Rendered with GPU and CPU.

None of these seem to make a difference. 

I don't believe this is z-fighting because no faces intersect with each other ever. 

I am on a very tight deadline and I can't find a solution.  Please let me know if anyone knows a solution.

Dropbox link to the Blender file: https://www.dropbox.com/s/9q2jf745go6u1l9/flickering_problem.blend?dl=0
Well you have a scene lit by three sun lamps which is not very conventional, but that should not cause problems by itself.

The real source of the problem is that your lighting seems inconsequential and  the lamp placement random and not well thought out.

You lamp objects are intermittently inside and outside of animated objects. That will obviously lead to seemingly random lighting variations across frames.