Not by itself but concentric and chiastic structure is a well documented feature of ancient Near Eastern literature, attested in Sumero-Akkadian, Ugaritic and Aramaic texts going back to the third millennium. The standard reference is John Welch’s edited volume Chiasmus in Antiquity, with dedicated studies of each of those corpora.
As for the flood narrative itself, the structure has been recognised by a range of scholars working at different levels of detail, Cassuto, Wenham, Anderson, Radday, and they segment the units differently but keep arriving at the same pivot, “God remembered Noah.”
The purported J and P texts by contrast do not have the same structure and the claim of interweaving of the sources is not symmetric so the idea that a redactor edited the sources into one that suddenly ended up with a chiasm stretching across the entire narrative does make single authorship more plausible.
The parallels to the Epic of Gilgamesh even more so. Take the birds alone. On the documentary account one source gives the raven and the other the dove, so each purported original Israelite source preserved only half of the bird episode, and the serial bird release that actually resembles the Mesopotamian one emerges only after a redactor combined the two halves. That asks us to treat the resemblance to Gilgamesh as an accident of editing, when the simpler reading is that the author used a serial bird release for the same reason the Gilgamesh poet did. Gary Rendsburg, who is no apologist, has argued the biblical flood tracks the Gilgamesh chiasm point by point and in the same order.