I've seen a variety of methods for printing reinforced drywall anchors, but haven't found one that printed reliably on my printer and did the job. So I've borrowed some ideas from those other places and created my own version in OpenSCAD.

The secret is the spherical pivot that stays trapped between the walls of the outer cylinder. Just shove a ramrod through the screw hole to pivot the arm into place and it will just stay there, held by the outer cylinder. This allows you to withdraw the rod. When you insert the screw, the tip will engage with the threads in the flip-arm, automatically align it, and draw it toward you until it pulls snug against the back of the drywall.

Print Details
Prints in one piece.
No supports needed.
0.3 mm layers
3 perimeters

I printed mine in PLA and they work fine for the relatively small things I've been hanging lately. If you are concerned about weight, you should probably use a stronger material like PETG or ABS. You could also increase the number of perimeters and give it more material to grab onto.

The provided STL is sized for a #8 wood screw, and requires a 1/2" hole in the drywall. I prefer wood screws because they have a deep thread that gets a good hold on the plastic. But the file is customizable, so you can adjust for different screw diameters if you like.

Installing
Once you've printed it, rotate the inner arm to free up any plastic overruns, then straighten it out again.
Drill a 1/2" hole in the drywall and push the anchor all the way into the hole.
Insert a kebab skewer or Allen wrench into the hole and push it all the way back until is flips the anchor arm into position.
Remove the poker and insert a wood screw. You should feel the tip grab inside the core of the flip arm.
Turn the screw until you feel the anchor arm snug up against the back of the drywall.

Pro Tip: As long as you remember to free up the swivel action first, this should be pretty  easy, but you may want to play with it in the open air a few times to see how the arm moves and how it feels when the screw grabs the threads.