The parts you have provided look a little like the two halves of a smoke detector; a flat circle with a short cylindrical flange, and a cone with two cylindrical flanges. It's not clear how the second part attaches to the first, and there's no indication of how large a moment the joint has to withstand.
Smoke detector housings sometimes use an interrupted multiple start thread, often with a snap lock feature at one end of the ramp, or a radial snap fit with axial slits in one or both flanges so they can be disassembled with either a twist or a vigorous yank, respectively.
Screw threads can be difficult to mold complete, because the core has to unscrew from the part somehow when the mold opens. However, an interrupted thread, or three or four interrupted threads, can be easier to mold, because the male thread can be formed directly in a simple two-piece mold, and the female thread can be molded with radial slides for ejection.
Two axial flanges, as you have sort of shown, given a traditional snap fit, can be difficult both to assemble and to disassemble, because of the large hoop stresses induced at assembly and disassembly. Axial slits/notches in one or both flanges greatly reduce the force required because the snap fits then induce only bending in what amount to crowned tabs instead of expanding the entire hoop.
To get a feel for what you face, you might prototype the assembly by machining a snap fit flange in two round plates of Delrin, then attempting to assemble them, then cutting radial slots in one of the flanges with a razor saw. The more slots you add, the easier it gets.
Failing the budget to do that, find some topologically similar joints in consumer products and do some comparative anatomy.
Mike Halloran
Pembroke Pines, FL, USA