The problem with the Genesis account of the Flood and that of evidences found is that the timeline of the Bible don't correlate with any of the dates.
From what can be calculated, Noah's Flood happened around 2104 BC, to precise, which a little over 4000 years ago, if we are to believe years are to be correct.
As to the Black Sea's Deluge. The timings are wrong; Noah's flood happened too late to coincide with the Black Sea flooding. The Black Sea Deluge happened around 7600 years ago, which would make it 5500 BC. This is roughly about 3500 years before Noah's Flood.
And the Black Sea was a more regional disaster than a global catastrophe. If the sea level was really lower than the time of Noah, then 40 days of heavy rain could not have possibly flooded the entire earth, no matter how stormy the weathers were.
There were no evidences of any major floodings around the Black Sea or in the Mesopotamia around Noah's time. Noah's Flood coincided with the 3rd Dynasty of Ur (c. 2112c. 2004 BC), the last major Sumerian city-state of importance. So earlier rulers of 3rd Dynasty were contemporary of Noah and his Flood, but there is no evidence of any major flood in Mesopotamia at any time during the 3rd Dynasty.
What I find strange is that Ur, and other Sumerian cities, like Nippur, have poems written about Ziusudra, the Sumerian flood hero, and mentioned in Sumerian version of the Gilgamesh's tale. These are the older than Noah's Flood itself. The poems indicated the Flood having happened hundreds of years before the reign of Gilagamesh (flourished 2700-2650 BC), therefore the Sumerian flood happened pre-2700 BC.
The Sumerian myth of Ziusudra also build the boat for wife and some animals too. It was the Sumerian god Enlil who initiated the Flood, but it was Enki who instructed Ziusudra how to save him.
Myths of both Ziusudra and Gilagamesh came from oral tradition, where the extant poems were derived from. Thus their myth is even older than the 3rd Dynasty of Ur.
Evidences of both Ziusudra and Gilagmesh can be found as far back as 2450 BC, where their names inscribed in tablets, but make no mention of Gilagmesh's adventures or Ziusudra's Flood, it does however indicate how popular Gilagmesh and Ziusudra were, during the 1st Dynasty of Lagash, when Sumerians began writing religious hymns and literature of their past, using oral tradition. The dynasty fell to the Semitic people, the conqueror of Sumer, whose first ruler is named Sargon of Agade; he founded the Semitic dynasty, the period of Sargon and his successors were known as the Akkadian Dynasty (c. 2334c. 2154 BC).
