if i understand this correct, you can create the flat spiral large enough so it fully covers your contour. Then Split the spiral with the contour curve. To get hold of the spiral parts inside the contour, use SelBoundary, select the contour curve and invert the selection to remove all curves outside the contour.
I think he wants the thing to spiral inward following the contour - sort of like a spiral CNC pocketing toolpath… Rhino does not have this kind of function…
But it`s not a spiral, it is an offset as shown in the above picture. @Manolo the offset distance it uses is the last distance entered in the Offset command.