Omega Cancer,
What you are attempting to do is draw a curve on the graphics sprite that all UIComponents inherit. That is not going to work the way you want it to. In you code you create a new com.esri.ags.Graphic, to actually have that graphic draw in map coordinates you will need to set it's geometry property to some actual com.esri.ags.geometry object like a Polygon. Polygons and Polylines are made up of Rings or Paths which are just point arrays. I don't know of any true curve capability in the AGS Flex API.