We have shipped finches from the US to the Virgin Islands. There is some work that had to be done on both ends. From the US side you have to get a vet health inspection, certificate, a bill of laden accounting for all of the finches in the shipment. From the Virgin Islands side the recipient has to get an import permit, pay import fees upon arrival, and be at the cargo facility upon landing or risk the shipment being destroyed by local authorities thinking the shipment is abandoned.
I would contact Hatian officials and see what their requirements are for importation. Their regulations will likely differ, since they are a different country and your looking at poultry.
Another way around the importation of live animals you may be able to import fertile eggs for incubation instead and ultimately achieve your goal. This may also work for long term operation of raising meat birds until you could get your flock breeding for you.
Good luck,
Sean