[OriginalIntent]

To flood the entire Earth to the depth of Mt Everest ...

How high were the mountains in the past?

Most who assume there was a Noah's flood also think the mountains were not nearly as high before the flood.

The catostrophic geological events during the flood may have caused rapid rise of mountains and sinking of valleys and ocean floors.

This rapid change in elevations expedited water, mud and debris drainage into the much larger new ocean volumes, (width and depth).

Agree with them or not, they do not generally make the argument you are describing.

[GonzoGOP]

OK, just for argument lets cut the height of Mt Everest from 8.8km above sea level to 4.4 km above sea level. Now you only need to move 1,153.22 cubic kilometers of water per second. Still much worse than being hit over the head with Niagra Falls. But to complicate the problem you now you now need to move enough rock to shove the Himalaya, Andes, Rockies 3-4 km into the air in only a few hundred years, since they haven't moved much since written history started.

And you still have to explain how a wooden boat stays afloat on a sea while being hit over the decks by Niagara Falls and having Mt Everest come up from the bottom. The energy release needed to move that much water and that much rock is going to sink the ark in short order. The amount of energy released is just mind numbing. You dump that much energy onto a planet and everything dies. And no wooden boat, no matter how well built, is going to save you.