You would just need to submit a picture on this thread for Indy to make into an avatar for you (preferably sized to 100x100 already, so it's less work for her).. She'll avatar-ify it, and give you a code. Then in your RS Linkify options, you just put that code in
The codes are visible in the avatar gallery yes, and technically anyone can use the picture, but if someone was to 'abuse' the picture, it can quite easily be deleted from the gallery and Indy's website.
Edit: If you don't want the picture to appear in the gallery I'm fairly sure that is possible, but it won't stop people getting the code by simply right clicking the avatar.
I just had a problem with a cross-domain request and thought it was because of a browser security update. Turns out AngularJS's $http service was modifying something in the request headers which was giving server response errors.