Favicon can see at beside address bar which indicates your blogger symbol either, it is a image or scrolling text.
Just in two parts you can 'add animated favicon to your blogger or website':-
PART1
Go to favicon generator
Now at the bottom page you can see upload image and scrolling text,after adding click on generate favicon button.
After getting favicons copy image location by left click on image (or) Upload to picasa or photobucket and copy link.
PART2
Go to blogger->> Design or Template ->> Edit Html
Now search below code by using shortcut key Ctrl+F
<b:skin>
Add the below code above <b:skin>
<link href='YOUR FAVICON URL LINK HERE' rel='icon' type='image/gif'/>
save template you are done.
