Do you honestly think there is limited long haul airliner/cargo capacity out there at present? A global airlift plan will be required, as it was for PPE, but the capacity is there, it just needs organised. BA won't be bringing back any 74s.
The major difficulty of mass distributing a vaccine is the public health infrastructure on the ground, not to mention the publics willingness to actually be vaccinated - not the distribution between countries.