How Flip Flappers is using a world-building technique from science fiction
Science Fiction has an information problem. When you set a story in the modern era, your audience already knows a great deal about the setting and how things work; they already have a good picture of what the world looks like. But when you set your story in space, or on an alien planet, or in the future, the audience starts out knowing very little about the setting and so you have a lot of information to communicate to them; you have to create the world for them. Even if you keep the amount to a minimum, you're going to need to feed them some information just so they understand what's important to your story, to at least sketch out the world around the characters and the dialog.
When science fiction was a young genre, back in the 1930s and 1940s and 1950s, authors lacked good ways of dealing with this problem and the result often wasn't pretty. But as time went on, SF as a genre developed a bunch of techniques for giving out information to the audience. The evolution of these techniques is part of why old SF stories can now feel clumsy and clunky; what was once the only way of feeding information to the audience is now the way that's only used by people who can't write better (or who don't understand how SF does it).
One of those tools is a trick that gets called 'incluing' (a term coined by Jo Walton, see also). In incluing, you put things into the story that don't fit into the normal world; these are the clues, little pieces of information that the audience will assemble in their heads to build a picture of your SF world. You don't necessarily do anything overt to draw attention to your clues, you just scatter them casually, in passing, through the story. They're just there, waiting for your audience to hit them and have their eyebrows go up. Incluing can work in any medium but is in some ways easier in visual media because it's easier to put things in the background; you don't have to mention the two suns, just have them in the sky. Want to communicate 'alternate world'? Have a bunch of dirigibles floating around in the background of a scene (yes, it's a cliche).
(Jo Walton describes this better and at more length in her article SF reading protocols, which is well worth reading in general.)
If this sounds a lot like how Flip Flappers has operated over its length so far, well, that's not an accident. Flip Flappers is actively using incluing and has been from the start. It has consistently thrown out of place bits and pieces at us in passing as part of its world building and has counted on us, the audience, to assemble the clues and work out their meaning and their place in the world over time. This is a brave thing to do, because it requires the audience to trust that the weird things mean something and are worth paying attention to, and to be blunt a lot of shows have betrayed that trust over the years by including weirdness that turned out to mean nothing and was just there to look cool. But Flip Flappers is willing to bet we'll trust it and the results are spectacular. It doesn't have to pause to explain things; instead it steadily builds up a world one piece at a time, expanding our understanding step by step. And in the process it can promote a character from the background to an important focus.
(This is different from using repeated motifs and symbolism, which Flip Flappers also does, in that we are supposed to actively notice the clues whereas the repeated motifs simply sit in the background, mostly below our awareness. The clues for incluing are explicitly out of place, or they wouldn't work.)
Most anime shows don't do this, for various reasons; the usual ways of explaining a show's world are much more overt, either visually or in the story itself (and sometimes both, of course). Flip Flappers is a rare show that is quite a SF anime not so much in its setting but in how it tells its story (although Flip Flappers' setting of course also includes SF elements).
(Looking back, much science fiction anime doesn't really use incluing very much. I have theories on why, but that'll have to be another entry.)
I suspect that Flip Flappers' significant use of incluing is one factor in some very polarized reactions to it. If you do trust the show, as I do, it is doing great work to subtly illuminate its world and explain things. If you don't trust the show, it is throwing pointlessly weird stuff at you and obtusely refusing to explain itself. We're both watching the same show and seeing the same things, but we interpret them differently.