It seems like the path is relative to the KML file being opened. I still can't get the icon to diplay when referencing a styleUrl. The sample you uploaded seems to have an extra <styleUrl/> tag right after the <name>201</name> tag. Anyway, I replaced that with
and I got my icon to display. It has a red extrude line to ground (water), and I can verify that as I zooom around, the Icon is wiped out temporarily by the polygon being redrawn. Seems like a render priority problem to me. I have no idea where to set render priority in this SDK, but the icons and extrude lines should be way higher than transparent polygon shapes.