There are numerous difficulties with the Jurassic Park scenario.
1. We do not have any way to get a complete set of dinosaur DNA. The movie/book addressed this by mixing in DNA from other species. They picked an obscure species of African frog so they could have a forced plot point later. (Dumb, Mr. Chrichton, dumb, especially when you could have used parthenogenesis to have the same plot twist!) This doesn't really work, though. You could mix in other things, and you might get something close to a dinosaur, but more than likely you wouldn't.
Getting dinosaur DNA at all is rare. Insects fossilized in amber do not have a good supply of functional Dino DNA despite the film/book. Blood drinkers digest their food very quickly, while being covered in amber takes a while. They've digested your sample! Even if they somehow didn't, the bacteria inside them will corrupt the samples.
But, suppose, despite all this, you found some intact blood in an insect trapped in amber. Okay, what is it? Blood drinkers aren't very picky about where they get blood. Is your sample a T. rex? Diplodocus? More than likely it isn't from a dinosaur at all, they did not have the world all to themselves! And you can't really tell without sequencing the DNA, which destroys it, oops! Can't clone that! Wouldn't work anyway, we have no T. rex DNA to compare it too! Okay, so the only way to see what we've got is to actually clone it. But we can't, because...
2. No mother. Organisms do not come to term on their own. Even egg laying species need to have the proper envirionment for the embryo during egg development. Without close dinosaur relevatives, we have nothing to create the eggs nor anything to study the egg development to make them ourselves. But, by point #1 above, we don't know what our sample is unless we sequence it, and that would destroy it! If we sequenced it, we could tell if it was a mammal or a reptile or what, but that's not a specific enough mother. The whole thing bogs down to an impractical mess.
It's possible that future technological advances will get around some of these problems, though I cannot imagine how. I expect time travel will let us see dinosaurs before genetic engineering.
And, no, I don't really think time travel is happening anytime soon either!