First off, consider that some shapes can't be laid out into a flat shape without some stretching of the material. So you can lay a cone out flat, but not a dome. A helix shaped plate won't lay out perfectly into flat shapes. But if you cut it into short enough sections, you should be able to get close.
My approach would be to take the theoretical auger shape and divide it into narrow radial strips. Each strip is a 4-side section polygon. Calculate the diagonals of that polygon in place, and then layout out a flat figure with the same sides and same diagonals. Doing this repeatedly should generate a shape closely approximating the auger in question. It may be helpful to calculate the points in Excel and then import into AutoCAD. It will still be tedious.
(Note that due to the surface not being exactly developable, that both diagonals can't be transferred exactly to the flat surface.)