State Health Flexibility Act of 2017 This bill amends the Social Security Act (SSAct) to replace federal requirements for Medicaid and the Children's Health Insurance Program (CHIP) with health care block grants to states. A state may use block grant funds to: (1) provide health care services to indigent individuals; (2) fund risk adjustment mechanisms for the purpose of subsidizing the cost of private health insurance for the high-risk population; and (3) support other welfare-related programs, as specified by the bill. In addition to repealing titles XIX (Medicaid) and XXI (CHIP) of the SSAct, the bill repeals: (1) the Patient Protection and Affordable Care Act, and (2) the Health Care and Educational Reconciliation Act of 2010. With respect to an alien not lawfully admitted for permanent residence in the United States, a state may use grant funds to provide only emergency health care services, as specified by the bill. A state shall contract with an approved auditing entity for annual audits of its grant fund expenditures. The bill limits the authority of any federal agency to supervise a state's use of funds received under the block grant program.