I'd appreciate someone checking this out for me because me and numbers have "issues" with each other.
Using the radius of the Earth I've calculated the volume, then using the radius plus 4000 metres I calculated it again (Everest is approx 8000 metres). The difference between the second figure and the first figure gave me the volume of water required to cover the Earth's surface completely.
I'm not claiming accuracy here, more of a rough guesstimate, a ballpark number and it comes out at 2046 million cubic km. To help get an idea of what that means, the Earth's crust is estimated to be 1332 million cubic km (I googled that).
Even if it's argued that the mountains weren't as high at the time of the supposed flood, you're still talking about alot of water.