Question: This question stems from a commonly depicted mode of transportation, the ornithopter. It is the primary flight tool in the latest Dune movie as well as seen in Black Panther and in several books I've been reading. My question is where did the idea for this flying machine first stem from as it seems to be a primary mode of flight for futuristic societies.

Edit: while the comment does answer where the name comes from and its design. I am specifically looking to the dragonfly design that has become associated with the name.

Answer: 
As Valorum pointed out, experimental ornithopters date back at least to [Leonardo da Vinci](https://en.wikipedia.org/wiki/Ornithopter) and probably earlier. Working ornithopters have been built in the real world; I used to have a toy that flew by flapping light Mylar wings. [Google Ngram Viewer](https://books.google.com/ngrams/graph?content=ornithopter&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Cornithopter%3B%2Cc0#t1%3B%2Cornithopter%3B%2Cc0) shows that the word *ornithopter* dates back at least to 1866, though it didn't "take off" till after the Wright Brothers' successful flight with a fixed-wing aircraft in 1903.

But all of that's in the real world. Presumably the OP wants to know when this concept entered science fiction. Obviously, Frank Herbert's *[Dune](https://www.isfdb.org/cgi-bin/title.cgi?2036)* (1965) made use of ornithopters, but he wasn't the first. In 1964, Cordwainer Smith mentioned "police ornithopters" in his short story "[The Dead Lady of Clown Town](https://www.isfdb.org/cgi-bin/title.cgi?41502)". That probably isn't the first use of ornithopters in science fiction either. I'm not counting the ancient myth of Daedalus, who was said to devise wings made of feathers and wax, because his invention doesn't seem to satisfy the definition of an ornithopter as a machine that flies by flapping its wings.

As to ornithopters that use the dragonfly instead of the bird as a model, in film they include *Stars Wars: Episode III, Revenge of the Sith* (2005), in which Wookiees fly [Raddaugh Gnasp fluttercraft](https://starwars.fandom.com/wiki/Raddaugh_Gnasp_fluttercraft/Legends). In written form, as pointed out by coppereyecat, they go back at least to James Gurney's *[Dinotopia: the World Beneath](https://www.isfdb.org/cgi-bin/title.cgi?24126)* (1995). The author discussed his inspiration in a 2009 [blog](http://gurneyjourney.blogspot.com/2009/08/insect-vehicles-part-1.html).
My great grand father the french engineer René Riout devoted himself for three decades to the realization of flapping wing ornithopters. In 1905 he invented his first models. In 1909 he won the gold medal in the Lépine competition for a reduced model. In 1913 he worked on the development of a model ordered by a pilot, the Dubois-Riout. The tests were stopped in 1916. In 1937, he finalized the Riout 102T Alérion, certainly the most successful piloted flapping wing ornithopter until the second decade of the 21st century. Unfortunately, the conclusions of the wind tunnel tests were not favorable to the continuation of the project.
[Ornithopter Riout 102T Alérion](https://en.wikipedia.org/wiki/Ornithopter#/media/File:Riout_102T_Al%C3%A9rion_by_Ren%C3%A9_Riout_France.jpg)
You have more image on [W.Pearce Riout 102T Alérion Ornithopter](http://oldmachinepress.com/2017/11/20/riout-102t-alerion-ornithopter/)
**Doesn't it look like Dune Ornithopter?**