What came to my mind at first were that you could use 2 cloud nodes,
with one not seen in the beginning and ending like the first one that is disappearing in the end.
Or easier just transform 1 cloud node in Y 360 degree like in the second example.
There are many more options you can use for the animated look of course. But this should be good probably for the first step.
Have a look at these examples. I don't like uploading animated GIF's as they are a littler bigger but i hope Matt don't mind these.
You can use X and Z too for animation of course but they look more chaotic in short videos.
Take care of the linear animation of keyframes or you will get slowing up and slowing down animation like in this 2 cloud example