I use my Flair image on another site, and I noticed that my reputation score there is not updated.
Since a picture is better than 1000 words:
Is this a bug or a feature?
Flair is updated every 24-36 hours. Just wait.
It also seems that the rate of refresh depends on the theme of the flair, i.e. the state of flair differs between themes as demonstrated in the screen shot: