Well, there's not really a lot one can say against that, aside from insulting religion, and I don't believe in doing that. Nicely done for admitting the faith bit though, it's better than most of the other FE'ers who tend to ignore the evidence for no good reason...
Although I will say, flooding the entire earth would definitely leave a trace in the geological record!
To answer your question.
It is thought mammals were beginning to evolve in the Cretaceous, while dinos were still dominant. They were wiped out, but some mammals survived. A mixture of a change in environmental conditions, and the presence of these mammals meant that they evolved, not dinos again - the mammals had a head start, as it were. From there, they differentiated into various ancestors to what we have today, and some that no longer exist in any shape or form.
But to be fair, the precise mechanisms are unknown, and science admits it. What we do know comes from stratigraphy, fossil evidence and dating techniques.
EDIT: Dino, if you want, there is a large Dinosaurs thread, where James's theory is properly discussed. Have a read, and have a laugh. Sorry James...