To do this the cutout black silhouette is in two identical layers, between which is sandwiched a thread. The ends of the thread are secured to the front of the card above and below the cutout window (the front is doubled layered too to give a neater final appearance with no loose ends being visible). The figure could then be "wound up" before being put in the envelope so that when it was taken out it would spin within the window.
The design itself I did in illustrator and cut out using my vinyl cutting machine, it takes a few passes to cut through heavy card and usually needs me to finish it off by hand too. I'm trying to think of other designs I could use for the spinning insert now, any suggestions welcome!