I don't have a particularly high score in the Chrome Dinosaur game, but I've managed to get over a 1000 before. I find playing this game on a laptop with a decent mouse is the best way to get a decent score.
I think the main skill required is quick reflexes and timing the jumps just right. I usually try to speed up the dinosaur as soon as I see the first obstacle, and try to keep the speed up as much as possible.
It also helps to experiment with different routes, taking small jumps if needed - don't be afraid to go off the beaten path.
For some tips and tricks to improve your score, take a look at this guide: https://www.ranker.com/list/chrome-dinosaur-game-tips-and-tricks/whatswithjeff. It gives some great strategies to maximize your score in the game.
