Advancing Access to Precision Medicine Act This bill allows state Medicaid programs to cover DNA sequencing clinical services for certain individuals. Specifically, states may cover such services for individuals under the age of 21 (or a lower age, if the state chooses) and for former foster youth under the age of 26 who (1) have been referred or admitted to a pediatric intensive care unit and seen by a medical specialist for a chronic or undiagnosed disease, and (2) are suspected by a medical specialist to have a pediatric-onset genetic disease. The Centers for Medicare & Medicaid Services may award grants to assist states in developing plans to cover such services. Additionally, the National Academy of Medicine must study the effects of genetic and genomic testing and ways to expand health insurance coverage of such services, including under Medicare and Medicaid.