Animated images are .gif format. There are many .gif files on the internet, but remember that they have to be 50x50 pixels. You can make your own but that's a whole different story.

Search google for "gif avatars" or similar and find ones that are 50x50 pixel image sizes.
Copy the image location in to where you choose your avatar and boom, new flashing avatar.
There's a good chance that what I've written above is useless and if you take any of the advice it's your own fault.