The current overall chain of command for the national supply chain seems to be:
(1) Federal Emergency Management Agency (FEMA) supply chain task force, lead by Rear Adm. John Polowczyk.
(2) Jared Kushner’s private sector team, which also seems to be working closely with the FEMA team. Kushner is the liason with the FEMA team to the White House, and can relay requests from Trump / others to the team.
The supply chain task force is providing resources in several ways. It is coordinating the airlift of materials from abroad to the US from private supply firms. Some of the materials it is buying for itself, for the FEMA stockpile, but most of it is still in the possession of the medical supply firms. The medical supply firms are then filling orders like normal, with no priority system.
As to how FEMA is distributing supplies, it seems that they are tapping into the private data on where materials are going, and they can see a little bit which areas need more supplies. They are then sending supplies to the places that need them the most. Before sending supplies from the stockpile, i.e. ventilators, Kushner is asking about utilization rates.
On April 2nd, the White House gave an update of the supply situation at the daily press briefing. So far, the US strategic stockpile has sent out: 27.1 million surgical masks, 19.5 N95 masks, 22.4 million gloves, 5.2 million face shields, 7,600 ventilators.
Production in the US is usually 30,000 ventilators per year, but apparently by end of June we will produce 100,000. In April and May, several thousand will be available each month.