You do know that Scamp
made them in their factory and sold
them as a factory option up until a few years ago, right? The large majority of Scamps from the early/mid 90's or so were sold
with the screen door option, and they look DIY because they are made with common hardware store parts. It was only very recently (2015) that they switched to an outsourced roll-out screen from Plisse.
I don't think there is a general pattern out there because very few are actually homemade, and variations of door shape and size are such that most have to be custom fit to the application.
The basic procedure is (1) box in the door opening with 1" stock on the inside to make a flat, rectangular, vertical opening, (2) make the two screen panels to fit the opening, (3) hinge the two panels together, (4) attach with hinges to whichever side of the frame the door will fold toward, and (5) add pulls and a catch.
Step one is the hardest, and it will be different for each trailer. It usually involves cutting pieces of wood to fit the curve of a particular trailer. You also have to figure out how to attach it to the shell. Scamp's version has a sliding roller track on top. Most of the DIY imitations I've seen left that off. It's not essential. Some people use piano hinge; others (like Scamp) use several small box hinges.
If you have a chance, look at a Scamp
first hand. There are plenty out there with the factory bi-fold screen door, so it shouldn't be hard to find one to check out. The principle is pretty simple, but the actual execution to fit a particular trailer takes some finesse.