Hey Peter 
Can you take a quick look at Include images and fonts in themes and components (You can stop reading when you get to the “Including assets in remote themes and components” section!)
Basically what you will want to do is upload the image file to your main theme. As you’ll see in the topic I linked, there will be an “Uploads” section where the file will be listed with its variable name and direct link. What you can do is right-click on the direct link and copy the link. If you paste it into the avatar flair image field on the groups page, you should be golden!