Trump has said that he plans on using military logistics to distribute the vaccine:
The U.S. military is ready to help transport a COVID-19 vaccine around the country as soon as one is approved by regulators, President Donald Trump claimed in Tuesday night’s presidential debate. The speed at which the president wants to distribute the vaccine, and the need for ultra-cold storage, suggests Air Force cargo jets might be part of the logistics solution.
“We’re going to deliver it right away. We have the military all set up. Logistically, we are all set up,” he said. “We have the military that delivers soldiers, they can do 200,000 a day. They’re going to be delivering.”
Though this seems to be as specific as Trump has gotten about this.
Worth noting is that while this is what Trump has said he was going to do, the Department of Defense seems a little more skeptical of this (same source as above):
The Department of Defense, which is helping coordinate Operation Warp Speed with the Department of Health and Human Services, insists that no significant use of military transportation is anticipated to ship vaccines.
“Our best military assessment is that there is sufficient U.S. commercial transportation capacity to fully support vaccine distribution. There should be no need for a large commitment of DOD units or personnel to support the nationwide distribution of vaccines,” spokesman Charles Pritchard said. “Any DOD-required support would be by exception. For example, military air assets may be called upon to deliver vaccines to a remote location only if no other means of transportation is feasible. However, there are no details yet on if that option will need to be used during distribution.”
So it appears that may not even be necessary.