Draconian - It is a png-apng image (animated png).Your browser may not support them.Try FireFox.
Pirate - You need to first
1) Create a new document with white background.
2) Open your smoke ring image in Gimp (File>Open as layers )
3) Now render the smoke rings out of the image.Place one each on a separate new transparent layer.
Try color to alpha, choose black. Or use a different layer mode to hide the background.I think it is multiply but not sure.
4) Delete the original smoke ring image you rendered the rings from.
You should have (however many ring layers you want) and one white bg layer.
5) Make them all invisible except the one you are working on.
6) Alpha to select one ring on a layer and run reflex (be sure to select 1 layer in the reflex dialog)This way Reflex runs and places all the layers together or merges them into one layer.
7) Make that layer invisible and do the same with the other ring layers.
8) When all the layers are ran through Reflex, make all invisible except one layer.
9) Arrange the rings (layers) how you want them to show in the animation.
10) Do an alpha to selection on the ring in the layer you have visible.Run Filters>Animation>Wave (about 6 layers the rest of the values leave at default).
11) Make all those layers invisible and make the next size ring layer visible and run Wave again.Do this with all the rings you want to animate.
12) Now make sure your WHITE background layer is on the bottom.
13) Now make all layers visible.
14) Run Filters>Animation>Combine Background (you need this script from Saulgoode).
15) OPTIONAL - Now delete the WHITE background layer unless you want to keep it.
16) Go to Filters>Animation>Play Back - select the play button and watch the animation.Move the layers according to your needs.
That is about it for a basic animation for rings.
Hope that helps.