We’re still tinkering with the flair / trust level icons here. I agree animation might be too annoying, considering replacing with static icon soon.
But the general idea is that trust level gives you an idea of how long the user has been around, I.E New → Trust 1 → Trust 2 → Trust 3 → Trust 4.
The flair is more of an award for special users, I.E iX staff, Moderators, Long time Contributors, etc.