Its not dinosaurs that produce oil. Most oil fields were likely large swamps in depository basins or on continental margins or maybe very shallow anoxic coastal waters under certain conditions. Go to somewhere like this today and you have enormous amounts of decaying organic matter that settles in them. Then for whatever reason these swamps had their organic matter "capped" by other erosion deposits that form an impermeable barrier protecting them from the atmosphere. These in turn are buried under sedimentary deposits and the heat and pressure deeper in the earths crust forms oil. Today we can mimic this process industrially through various means whether its using natural gas as a feed stock, you can use coal or even in theory decaying organic matter. The thing is though for widespread application it cannot compete with the natural deposits we have.

Because of our oxygen atmosphere and high UV exposure from the sun it makes hydrocarbons unstable in our atmosphere there are only certain geological conditions where this process can happen.