This Customizer can make any drawn shape into a slinky, also it includes a generator for stars and polygons, a polygon with a high number of points becomes a circle. The profile includes a separator between the coils to minimize the surface they can stick together and make them easily separable. With the default settings and 0.2mm print resolution I was able to separate the individual coils by hand, though it is faster and easier with a knife or a spatula.
When setting the separator thickness to 0 the profile becomes a rectangle again.
Supports should only be enabled from the platform, between coils it is not necessary. Small parts may produce self-intersecting surfaces, this may cause problems with some slicers. For Simplify3D the setting "Merge all outlines into single solid model" should be used.
The cat used as default was converted from this OpenClipart: https://openclipart.org/detail/1198/cat-silhouette
I used the Inkscape to OpenSCAD converter http://www.thingiverse.com/thing:1065500 and copy&pasted the created path into slinkify.scad.