You can read the biblical account of the Flood in Genesis 6-8. As you read this you will notice in Genesis chapter 7, verses 11 and 12 that the rain is almost an afterthought. The first two sources of water for the flood mentioned were the fountains of the great deep and the windows of heaven. Science has discovered hydrothermal vents at mid-ocean ridges in 1977. So it is easy to imagine fountains of the great deep being opened by God, allowing the pressurized water to contribute to the flood. Science has also proposed that the Earth used to have much denser clouds than it has now. Such a canopy would create a greenhouse effect, making the climate of the entire world very mild. Fossil finds indicate that not just the dinosaurs, but all animals, plants, and insects were much larger at one time indicating a superior climate. At the time of the flood, it would have been easy for God to allow this canopy (or a large percentage of it) to fall as water. If almost everything fell at once, it would not have been like rain, it would have been like opening the windows of heaven. The crushing splash of water would have quickly drowned all people and animals that found themselves suddenly and unexpectedly immersed in water.
By the way, this could explain the thousands of woolly mammoths that have been found perfectly preserved in polar areas some with food still in their mouths. Once the protective canopy and its greenhouse effect was gone, the world would have turned cold on the poles, freezing the mammoths in the water that killed them.