You can’t dominate with your putter if you don’t know how to aim it correctly or how much break to play. Nail these fundamentals first. If you hook or cut-spin your putts your chance of success goes down. If your putts roll off the face in the same direction your putter is heading immediately after impact that’s good. If your putter moves one way and the ball another you’ve got problems.
Adding to the difficulty is the fact that Shinnecock’s greens run faster than Flynn originally intended. Shortly after he redesigned the course in 1931 (Shinnecock dates back to 1891) the USGA began measuring how fast and far balls rolled on level putting surfaces calling the measurement “green speed.”
In my opinion the only way to develop this skill is through experience. Pros have the advantage of unlimited practice time but you can begin to catch up with a simple three-shot experiment that I use in my schools. Its entire purpose is to open your eyes to the various backspin outcomes that can be created by the type of lie you’re facing.