The American PPE Supply Chain Integrity Act This bill requires specified federal departments to purchase certain items, including medical supplies, personal protective equipment (PPE), and clothing, from the United States, with exceptions. Specifically, the bill requires the Department of Health and Human Services, the Department of Homeland Security (DHS), and the Department of Veterans Affairs to purchase items such as specified medical supplies (including disinfecting wipes), PPE, and fabric products (including clothing, bags, and tents) from products that are 100% grown, reprocessed, reused, or produced in the United States. The bill requires regulations to (1) prohibit the use by any federal department or agency of reverse auctions or lowest price technically acceptable contracting methods for the procurement of PPE if the level of quality or failure of the item could result in infection, illness, or death; and (2) establish a preference for the use of best value contracting methods for the procurement of such equipment. The bill applies the Berry Amendment (which requires the Department of Defense to give preference in procurement to domestically produced, manufactured, or homegrown products) to specified supplies and equipment, such as surgical dressing materials, hospital and surgical clothing, and textile medical supplies and equipment.