How accurate are those public blood pressure monitors and can readings be taken with a shirt or jacket on?

Depends: It depends on the size of your arm and if the machine is calibrated. It is going to be the most accurate if your arm’s diameter is “average” size. Small arms will read a little low, and big arms will read a little higher. It won’t read through a jacket, but a thin shirt is OK. It’s also important to sit 5 min before checking, and not be talking or texting etc when the machine is reading your BP.