If you can view the .gif URL from a browser and it animates, it should also work using that markdown.

I've seen where an animation on a page is not an actual .gif animation but where the page's javascript performs the animation by cycling through a number of static .gif (or .png or .jpg, doesn't matter) images. So linking to a .gif from that, would of course, only link to the one (static) image.

Without a link to an example of an image giving you trouble, I couldn't speculate as to what the actual problem would have been.