Hi x3sphere,
Thank you for providing this feedback/feature request!
Unfortunately the APIs where the avatar data at the Battlenet account level exist are not currently exposed via the Blizzard Developer Portal, so we are unable to satisfy this request at this time. However, we can document this request for future consideration.
For clarification, are you most interested in the avatar that the user has configured in the Battlenet desktop application, or are you more interested in a “pinned/preffered” WoW character avatar (i.e. the avatar shown on worldofwarcraft.com when logged in)?
Thanks again.