I can't read a flipping green to save my life.

Are you sure you are misreading the greens? I know it sounds stupid, but make sure you are aiming and putting in the desired direction first. For example put an alignment stick down the line of your putt when you are on the practice green. Because that can totally fool you. We are bipeds. Even without aimpoint we are usually very good at judging slopes, with our eyes as well as with our body. We would constantly be toppling over if it were otherwise. So before you start mistrusting the line you see (or feel), first mistrust your putting stroke.

Apart from that: read the green from outside to in. Slopes from bunkers and towards water hazards will have more of an effect than small hills and dells on the green itself, even though they might appear visually more prominent. So get a first view of the lay of the land before you even get onto the green.