Outside of Hollywood films, dinosaurs like Tyrannosaurus and Triceratops never coexisted with humans, and no case can be made that The Flintstones is an accurate depiction of prehistory. That has not stopped young-earth creationists from maintaining otherwise, though, and this has led to some rather silly statements.
Attempts to squeeze paleontology into a literal interpretation of Biblical timelines have a long history. A 1912 issue of Current Literature featured some excerpts from a book about paleontology called Evolution in the Past by H.R. Knipe. The article itself is not terribly interesting, but the captions accompanying the article's illustrations are. Several dinosaurs and extinct mammals are featured and each caption explains the benefits or dangers these animals would have posed to early humans. The caption beneath a pair of Iguanodon reads:
THE TERROR OF THE RIVERBANK IN THE GEOLOGICAL PAST
The iguanodonts fought with their tails, and in the course of the combat rendered life precarious in the vicinity for all living creatures. It is difficult to see how prehistoric man could have made his abode along the main streams while these monsters flourished.
In truth, early humans had nothing to fear from Iguanodon. The herbivorous dinosaurs had been extinct for about 114 million years by time the earliest humans evolved in Africa. To suggest otherwise would require some startling evidence indeed! It should be noted that the tone of some of the captions makes it seem like they are not to be taken seriously, but even if this is true they are not out of line with what many creationists truly believe. (Don't even get me started on their ideas about what Tyrannosaurus would have eaten in the Garden of Eden.)
If humans did live alongside dinosaurs, though, it does raise the question of how our kind survived. Why wouldn't our species have been consumed by a horde of hungry tyrannosaurs, or our early attempts at agriculture destroyed by herds of sauropods? There is simply no record of any kind of Dinotopia, and most of the "evidence" creationists offer are like Rorschach tests; they see what they want to see. Watching humans flee from dinosaurs might make for exciting cinema, but it is absolutely awful history.