I think adding position keyframes and slowly moving the noise to the right and slightly down looks the best. Then you’ll need to animate the noise position over time. The darker and lighter areas (the contrast) of the fractal noise is what will ultimately displace your flag. First, you’ll add a time expression to the evolution of your fractal noise (I like time*15 for the most natural look). Here you can customize the look of the waving of the flag. On the new solid, add a fractal noise effect. To do this, you’ll need to create a new comp, and a new solid. The core idea is to create a displacement map yourself. It provides one of the more realistic looks, and is by far the most customizable and professional looking of any of these looks. In the above video, Ignace Aleya does a great job of explaining what is perhaps my favorite way to do this effect.
