Is it possible to have an animated texture on a character's mesh

you could add a socket to the mesh and in the bp add a decal to the socket.

Say I wanted to have a teletubby like character with a looped 60 frame animation on a tv on it’s stomach, what would be the best way to go about it?

Your Animation is a movie? You can add it to the Project and create a Media Texture. This can be used as a Material in a Part of your skelMesh