To get the animation started do like this:
(Image1.Picture.Graphic as TGIFImage).AnimateLoop := glEnabled;
(Image1.Picture.Graphic as TGIFImage).Animate := true;
To control the animation speed, set the AnimationSpeed
property between 0..1000, default value is 100.
See also @DavidHeffernan's answer, How to use Animated Gif in a delphi form