Text can only have a single color. If you Google, you will find some kludges for e.g. making top half (or whatever fraction) one color, and bottom half another, by using duplicate strings and clipping.
You could do it by creating your text as an SVG graphic but using shapes for the text, rather than characters. (SVG can contain text nodes.) Then you can e.g. style the shapes using a gradient and you could animate the gradient. You can style SVG with CSS, if you embed the SVG directly into the document.
Use CSS animation, not jQuery Animate. jQuery animate is seldom the best way to to animation today anyway.
In any case, jquery animate can't do it.