To set a GIF animation as the background for the chess board, choose Settings > Board > Background > Choose GIF..., then choose a GIF animation and click OK.
Unfortunately, Chess will not detect the duration of each image's display in the original GIF. To set a framerate for the animation, see Choose framerate....
Additionally, this feature works best when each image in the animation is fully rendered, rather than optimized for size and performance.
For more animation options, Stop/restart animation.
The animation can be any size, and Chess will automatically resize it to fit the board (your original file will not be modified). However, you should try to make sure it is square, as it will be resized to fit a square, so the further it is from square, the more distorted it will appear.