I have never seen a parapsychology study, so I will go look for one. However does every single study have massive flaws in it?

Damien Broderick's Outside the Gates of Science summarizes a number of parapsychology studies, noting that several of the studies do indeed seem quite solid. It doesn't come to any definite conclusion over whether psi phenomena are actually real or if there's just something wrong with our statistical techniques, but it does seem like there might be enough to warrant more detailed study. See also e.g. Ben Goertzel's review of the book.