Medical Supply Transparency and Delivery Act This bill provides for the procurement and distribution of equipment and supplies needed to combat COVID-19 (i.e., coronavirus disease 2019). The bill sets forth responsibilities for the National Response Coordination Center (NRCC) of the Federal Emergency Management Agency, including that the NRCC must (1) direct the national production and distribution of critical medical equipment and supplies; (2) communicate with states, local governments, and Native American tribes regarding the availability and delivery schedule of equipment and supplies; and (3) make specified information publicly available. The Department of Defense may detail members of the armed forces on active duty or civilian employees to support the NRCC. The President, using authorities provided under the Defense Production Act of 1950, must establish a fair and reasonable price for and procure needed equipment and supplies. The Government Accountability Office must annually submit a report to Congress assessing the Strategic National Stockpile. The Council of the Inspectors General on Integrity and Efficiency shall designate an inspector general to oversee this bill's implementation.