What does the Bible say about the extinction of the dinosaurs?
Actually, the Bible says nothing about the extinction of the dinosaurs. If "behemoth" and "leviathan" (Job 40:15-41:10) are beasts like what we call dinosaurs, then they existed after the flood and possibly into the times of David and even Isaiah, who both refer to leviathan.
Some people speculate that the dinosaurs were destroyed by the flood, not having been saved on the ark Noah built. I have difficulty with that, since God told him to take two of "every" beast (Gen 6:19). However, I have heard one interesting theory that would indicate that the large animals prior to the flood ceased to exist as such after the flood. This particular biologist notes that men lived much longer before the flood than after (900 years as opposed to 70). He says that if lizards that we now know lived such a comparatively long time, they would grow to be the size of the dinosaurs. His position, then, is that it is possible the dinosaurs never died out; they just didn't grow as big. I'm not sure I buy his theory, but it does seem to fit with the scriptures.
Another theory, which probably holds even less water, is that the dinosaurs never existed. This theory says that God created fossils in the rocks when he created the rocks, but that they were fossils of beasts that never existed. The problem with this theory is, why would He do it? To test people to see if they would believe in Him even in the face of this seeming evidence?
In the end, I have to say that I don't know much about the extinction of the dinosaurs because the scripture just doesn't address it. The Bible is not intended to be a science textbook, and leaves a lot of details out that we now ask about.