Improving Access to Indian Health Services Act This bill permanently extends certain Medicaid flexibilities relating to Indian health care providers. Specifically, the bill permanently expands coverage to include clinical services that are furnished outside of a clinic by an Indian Health Service (IHS) facility, a tribe or tribal organization, or an Urban Indian Organization (UIO). Current guidance from the Centers for Medicare & Medicaid Services allows IHS and tribal facilities to receive payment for clinical services provided outside of clinics through October 31, 2021; facilities are expected to work with their state Medicaid programs to transition to other, more permanent payment options for these services. The bill also permanently establishes a 100% federal matching rate, also known as the Federal Medical Assistance Percentage (FMAP), for UIO services. Current law provides a 100% FMAP for UIO services during the eight fiscal quarters after March 11, 2021.