Best format to export to in blender
The first problem you have to solve is whether the flickering you see is part of your animation or part of the video encoder.  If you have bad normals in your faces, you'll see a flicker.  ProRes 422HQ produces a video file that's both low enough of a bitrate that most modern (post 2008) hardware can play without dropping frames, as well as high enough of a bitrate that you will not see any compression artifacts.  If you still see flickering, the problem is with your model, not your video encoder.  If you see no flickering, then start wandering through the settings of whatever video encoding format you are most likely to use for final product.  If the video's final resting place will be YouTube, that would be H.264.  If it's your laptop or desktop computer, it might be ProRes (Mac) or AVI (Windows) or Ogg (Linux).