High Risk Pool Flexibility Act of 2004 - Amends the Public Health Service Act to expand the definition of "qualified high risk pool" for grant purposes to allow a State to meet the requirement to provide all eligible individuals with health insurance coverage by utilizing an acceptable alternative mechanism that includes a high risk pool as a component and: (1) that provides for risk adjustment, risk spreading, or a risk spreading mechanism (among issuers or policies of an issuer) or for some financial subsidization for eligible individuals, including through assistance to participating issuers; or (2) under which each eligible individual is provided a choice of all individual health insurance coverage otherwise available.