The Dunaway Fold is the simplest way to make a slightly puffy, fringed shape with the edge of a pocket square.
Depending on how stiff and how colorful your fabric is, this can look something like a flower or a bursting firecracker.
The Dunaway Fold: Step 1
Rather than laying the square flat, pinch it at the center and let the edges and corners hang down
The Dunaway Fold: Step 2
Take a moment to adjust the hang of the fabric so that it is relatively even all around.
The Dunaway Fold: Step 3
Still pinching the center in one hand, use your other hand to tug gently on the dangling edges, pulling the pocket square into a loose tube shape.
The Dunaway Fold: Step 4
Invert the tube shape and spread the loose edges out with your fingertips, making a roughly symmetrical spread of the corners. Fold the center of the square upward, stopping about halfway up the tube shape.
Tuck the doubled-over tube into your jacket breast pocket so that only the splayed edges of the pocket square are visible. Adjust them with your fingers as needed. Perfect symmetry is not needed.