The problem with the Flood was that the historical sources that the Biblical historians had to work with were flawed. They indicated the Flood and humans survived the flood in an ark, but not how this happened. The inspiration from the Holy Spirit came in how they filled in these gaps to make this a Yahwist history rather than a pagan one.
The question is not how do we know this is right, but is it right? Does the revelation of God found in the story of Noah correspond to the revelation of God found in the rest of the Bible and in particular with that of Jesus Christ? That is a question you need to answer for yourself.
I will point out a part of the story that is troubling and that is the Curse of Canaan. As you know after the flood Noah got drunk and fell asleep in the tent naked. His son Ham saw him and as a result Ham’s son Canaan was cursed to being the father of a servile race.
While the taboo concerning looking at the naked parents may have been real, the penalty seems extremely harsh and strangely is applied to the son and not the father. What appears to be more germane is that fact that the Hebrews conquered the homeland of Canaanites. This curse was also used as a rationale for the slavery of Blacks in America who are descendants of Ham.
Thus there arises the question as to whether or not a self serving bit of tradition might have crept into this story that really did not belong. Again God did not curse Canaan, but Noah did backed up by God. I might mention also that the origins of the other peoples in Genesis tends to put the Hebrews in a good light.
It should also be noted that Jesus reversed the Curse of Canaan when He healed the daughter of the Canaanite woman after discussing with her whether He should grant her request.