Hi Anna!
Thank you so much for your question! What major for pre-med students to choose is a pretty common question we get, so I hope you will find this response helpful :). 
Personally, I know of two folks who are in the school of Kinesiology and intend to pursue a career as a physician. From what I have heard, I think it is a great way to learn more about the body in depth prior to medical school. I believe that there is at least one required anatomy class (maybe more, I am not 100%) sure. Taking an anatomy course is helpful for many pre-med students, because usually the first semester of medical school this is an extremely large component of the curriculum and a lot of folks start from square zero. If you have some anatomy experience, this will probably make that period in your life a little less stressful!
I just looked at a sample schedule for the Exercise Science major, and it looks like Stats 250 and Psych 111 are required–or at least recommended for the major. These two classes are also pre-med requirements. I believe Physics might also be a requirement for some Kinesiology classes (but don’t quite me on that). It also looks like there is quite a bit of wiggle room for classes that are not major related. You might just be taking a lot of science classes at one time–which is something a lot of pre-medical students do already. 
When we get asked questions about majors, we generally recommend for people to major in anything they are interested in. For example, I am double majoring in Sociology and Biology Health and Society, but I would consider my “primary” major as sociology. This is something that is not science related, but I decided to pursue it because I am extremely interested in it! So, if you are interested in Exercise Science, I would say go for it. But if you are only doing it because it would be a “good” pre-med major, then maybe take a step back and ask yourself if you think it would be the most fulfilling for you. You could always try one or two classes to see if you are interested. 
I hope this helps. I am sorry if it is vague–none of our advisors are currently in the school of Kinesiology. If you have more questions, please respond to this post or attend our zoom advising hours 6-10 Sundays through Wednesdays! 
-Cate, PMH Co-President