Unfortunately, there are really no available facilities to do blood tests yourself, most likely because of the nature of how they get analyzed and the specific items needed to collect the specimens, as well as being cost prohibitive and federally regulated for portions of the process.
For example, most blood tubes have some sort of additive to cause the blood to react in specific ways. A tiger top tube (red and black rubber stop) or the newer plastic version, the gold top, has a clot activator and a gel for specific serum separation. Once the blood is drawn, it is centrifuged, and then assayed in various ways, most of them involving microscopic counts and smears of various types.
In addition to this, there are various reagents and stains for blood tests that are necessary, most of which require some sort of facility type license (clinic, hospital, etc) to purchase. And, the last time I checked, the needles and other implements were also controlled, due to their possible use as drug paraphernalia.
Add to the list training, because if you are drawing different types of tubes, there are specific methods and order of draw to avoid contamination one tube with another, disposal of the body fluids and sharps after you are done, which is tightly federally regulated, with very hefty fines for improper disposal or infractions. Additionally, it is extremely awkward to draw blood on yourself, and an improper draw can result in exploded RBC's in your sample, which means you have to start all over.
There are various home kits that you can order for different tests, however they are somewhat cost prohibitive, and are of the blood spot, send it in type of test. I am not aware of any where you draw your own tubes and send them in, but I haven't looked at them in a while, that may have changed.
Your best bet would be to come up with something that you want to test/prove, research the literature to see if it has been done already, and then present it to a local college that has a doctoral level kinesiology program, and see if they want to take it on as a research paper.