Space1 has the largest known number of documented private space industry rocket launches. Year 2018 will see that number ramped up with the new reusable USS Pioneer rocket fleet. Since the beginning of accumulated time with Rocket Space Industries (see link), the early beginnings of the White Chemical Rocket launches and the invented Kinematic Rocket, the number has totaled 6,727 launches.
https://space1usa.blogspot.tw/2017/05/space1-rocket-launches.html