The Hebrews got their flood myth from the Neo-Babylonians (6th century BCE, during their exile in Babylon) or even earlier by the Neo-Assyrians (7th century BCE).
The Babylonian myths predated the Neo-Babylonian (or the Chaldean) dynasty, existing in the previous Babylonian dynasties, in the previous millennium(eg Amorites dynasty (1st dynasty of Babylon) with the Epic of Atrahasis and Epic of Gilgamesh), and the Kassite dynasty (2nd dynasty of Babylon), with Epic of Gilgamesh.
The Assyrians and Babylonians weren't just invaders, they also do trade, and at times, cultural exchange.
If they weren't executed after being conquered, royal and noble people would be hostages, were often educated in the culture and etiquette of their hosts, as the hosts would also learned from the hostages.
And if the priests of Judah were also hostages at Babylon, then they would have learned of their host's religion.
There are no evidence that Judah and Israel have any scriptural literature PRIOR TO 7th century BCE: Jewish & Christian traditions that books attributed to Moses as author, such as Exodus, Numbers, Leviticus, & Genesis, don’t exist in the late Bronze Age (c 1590 - c 1050 BCE).
There are no original Hebrew sources (eg Genesis, Exodus, etc) in the second half of 15th century BCE, the supposed time of plagues of Egypt and mass exodus out of Rameses (Egyptian Pi-Ramesses, “House of Ramesses”) and the start of Joshua’s & Israelite conquest in 1407 BCE. There are no mention of these events or people (eg Moses, Joshua, etc) in any Egyptian or Canaanite sources in this century.
In fact Pi-Ramesses (biblical Rameses) don’t exist until the 13th century, in which Seti I named the city which he started building after his father, Ramesses I, who was the founder of the 19th dynasty (1292 - 1189 BCE).
It is highly doubtful that Israelites have their own Flood story prior to 6th century Exile, because as I said earlier, Genesis didn't exist in the Late Bronze Age (c 1590 - c 1050 BCE).
As I said earlier, there are earlier texts and myths, older Babylonian sources to the myths of Atrahasis (eg Epic of Atrahasis, c 17th century BCE) and of Utnapishtim (eg Epic of Gilgamesh, c 18th century BCE).
The myths of Utnapishtim & Atrahasis were the same character, but just under different names, but they were based on older myths, in which the Flood hero was named in Sumerian as Ziusudra.
Ziusudra appeared in number of Sumerian clay tablets in the second half of the 3rd millennium BCE, hence Early Bronze Age (EBA is dated from c 3100 - c 1950 BCE):
- Fragments of clay tablets found in Eridu, in which it narrated the myth of creation and flood, hence translators and scholars often referred the tablets as Eridu Genesis. But only portions survived, eg
- humans were created by An, Enlil, Enki & Ninhursag;
- people drowned in flood water;
- and post-Flood when the smell of sacrifices drew the gods to Ziusudra
- Sumerian poem of the Death of Bilgames, where Ziusudra & the Flood are alluded to, but not narrated.
- The Instructions of Shuruppak (tablet dated to around 2600 BCE), a wisdom monologue from Shuruppak to his son Ziusudra.
- There are several Sumerian king lists, but only one, that mentioned Ziusudra and the flood, in the recension version, WB-62
The points of this history lessons in regarding to Ziusudra, Atrahasis & Utnapishtim, is the connection between Ziusudra and the Sumerian city Shuruppak, because there are real evidence that devastating flood hit Shuruppak around 2900 BCE.
This is where the legend of Sumerian and Babylonian myths developed from, based on a real river flood. As Genesis flood was based on Babylonian Utnapishtim, the Babylonians based their story on Sumerian Ziusudra...but myth of Ziusudra is based on real river flood at Shuruppak, not on the Black Sea Deluge hypothesis.
People who think the Genesis flood is based on the black sea deluge hypothesis is relying on flimsy false equivalence & confirmation bias.
There you go! 
