Wavy border

Use duplicate zig-zag paths, slightly scale down and adjust position of the top one, adjust stroke weight and alignment on both paths.

Peter

As mentioned Kurt Zizgzag Effect can do that. Just create a rectangle and use Zig Zag panel settings to create your artwork. Do not forget to expand abject if you want to separate it from rectangle.

The Width Tool will help you, or you could create a second fill of the shape with a transform to be larger and an offset to be slightly out of sync with the front fill.

Using a custom calligraphic brush is one way to achieve it. Possibly combined with Zig Zag.