Best way to create an airflow animation

There are some third-party plugins that could potentially make something like this easier (by generating multiple shapes instead of one at a time), but you can certainly do it with the native tools.

Using shape layers, you can draw custom paths with the pen tool, covering the full length you'd want each stroke to take.
Create an open path with Stroke, but no Fill. I'd recommend having the ends of the path extend offscreen / behind other objects.
The Stroke options now allow tapering, so with that and a rounded cap, you could get the exact shape of those strokes in your example. Adding a Trim Paths to this would let you restrict the visibility of each stroke to only a short segment, and the Offset property within Trim Paths allows you to easily animate that segment throughout the length of the path, making for easy looping.



Make a bunch of copies, updating the paths and varying the Offset property to create variety. Add some glow and maybe a few other effects to style it properly, and you're there!