Go to Dashboard | Khan Academy. And click your current profile picture next to your username.

Any available pictures will be listed. Custom pictures are not allowed on Khan Academy.

It's also worth noting that your avatar can only be changed from the desktop version of the site (this feature is not supported in the mobile apps).

You can find instructions for changing your avatar here: https://support.khanacademy.org/hc/en-us/articles/115007749488-How-do-I-change-my-avatar-