I remember a LHotP tv episode where a kid “borrowed” a neighbor’s front screen door to act as a sieve to pan the local river for gold with Laura Ingalls.
Turns out it was just Iron Pyrite…fool’s gold.
So the tech was available to Rural America in the Late 1800s.
I think David Simmons is onto something. Why try to eliminate flies from the whole house, when you’re going to see them everywhere else you spend (most of) your time, and can easily cover the few food items which need covering? The ideal of a hermetically-sealed house isn’t something many people from the early 20th century would recognise.
Lucky Nava in Spain gets dry and hot; I have spent many warm months in places like Amsterdam and Bruges and Ghent-- you know, humid towns with lots of CANALS. With no tradition of screened windows a living hell (I’m one of those mosquito-bait types). The Europeans do, however, have a marvellous plug-in mosquito death-ray device that works wonders by emiting a tiny bit of nerve toxin (made, of course, by Sara Lee!). At first I was wary, but then good nights’ sleep won me over. I’m a convert, but they’re probably illegal in north America. . . would probably kill the parrot. . .
I do think the hermetically-sealed household is a post 1950s concept and perhaps even a white American thing. When I lived in Hawaii it was just accepted that you shared your house with a variety of critters and you dealt with it in various ways. Washington state: “Oh my God, there’s a FRUITFLY in the kitchen!” Hawaii: “Huh. . . think that gecko in the living room will manage to eat that entire roach? Oh, would you put that rat outside?”
Not that you’d use the television show as a historic reference.
Speaking of flies …
I’m reminded of the story by writer H. Allen Smith.
A barber stood up one day, walked to the screen door and rippied it off.
When asked why he replied, “I finally figgered it out. That screen door just nacherly attracts flies.”
The folks in the recent PBS historical-reenactment series “Texas Ranch House” didn’t clean up soon enough after a big dinner party, and before long they had a fly infestation that looked like something out of the Book of Exodus. Yikes.
I should’ve added: the show was set in the late 1860s, and there were apparently no screen windows available at the time.
I looked up some things last night. I can’t find where or when they started making wire mesh/wire cloth/ wire gauze commercially, but it was clearly available at least on a small scale by 1815, when Davy did his experiments that resulted in the safety mining lamp. Those experiments, in turn, must have unleashed an industry in making mesh for those lamps )which were widespread as a result of Davy’s work), if one didn’t exist already. But it wouldn’t necessarily have resulted in window-size pieces of mesh.
When I lived in Denmark, the flies nearly drove me mad. In summer, they were all over the place, and every single morning a fly would buzz around my face and wake me up. I would hide under the duvet, and it would just lie in wait for me, buzzing around (I could hear it through the fabric). Argh! Danish people just didn’t seem to mind and watched in bemusement as my hostdad (a German) and I manically swatted flies.
Anyhow, I love our screens. We can keep the windows open all evening without getting zillions of moths and mosquitos, and we have the wonderful invention–a whole-house fan–so that every night and morning we can suck tons of fresh cool air into the house before it gets hot without also sucking in every bug in the neighborhood. (I think people only have them where there are very hot days and nice cool nights; I’ve never seen them anywhere else I’ve lived, but here everyone has them).
In the late 20’s the house, in a small town,
had a screened back porch. None on other windows.
In the 50’s window screens were rare throughout the rural south.
Word. In my experience the bug situation here in the Netherlands is nowhere near as bad as in my southern New Jersey swamp-riddled hometown, but it still can be annoying. (And yeah, Bruges on a hot June night is gawdawful bug-wise).
I appreciate the spiders that spin webs across the gap between the window sill and the raised window edge. Bug flies toward the light in the room, bug gets caught, spider gets meal, everybody’s happy (except bug, of course). I will probably always think of spiderwebs from now on as “Dutch window screens”. 
The mosquitos where you are must be wimps. Around here, the tend to get one’s attention.