American Financial Markets Integrity and Security Act This bill generally prohibits investments in sanctioned entities, certain Chinese military companies, and entities reasonably believed to be involved in activities contrary to the national security or foreign policy interests of the United States. These entities may not sell securities to U.S. markets. Investment companies, insurance companies, and retirement plans are prohibited from investing in these entities. The bill also prohibits the use of federal funds to enter into or renew a contract with these entities. Furthermore, the Department of Commerce and the Office of the Director of National Intelligence—in addition to the Department of Defense as under current law—are allowed to add entities to the list of Chinese military companies. Additionally, the Office of Commercial and Economic Analysis of the Air Force must (1) report on the strategic importance to the Chinese government of inflows of U.S. dollars to China through capital markets, and (2) make recommendations to mitigate any related national security and economic risks.