Here are the rules for importing hatching eggs to Canada.
3. General Import Requirements - US Animals - Other than ruminants
(1) An equine, swine, poultry, hatching egg, bear or non-domestic feline may be imported into Canada from the United States if the animal is accompanied by a certificate of an official veterinarian of the United States or a certificate of a veterinarian endorsed by an official veterinarian of the United States that clearly identifies the animal and states that:
the animal was inspected by a veterinarian within 30 days preceding the date of importation;
the animal was found by a veterinarian to be free from any communicable disease;
the animal was, to the best of the knowledge and belief of a veterinarian, not exposed to any communicable disease within 60 days preceding the date of the inspection;
the applicable conditions set out in the Regulations and in this Document respecting the importation of that species of animal have been satisfied; and
the animal meets the conditions shown on the certificate.
(2) An animal imported into Canada from the United States shall not be admitted into Canada if it has been in the United States for less than 60 days unless it is accompanied by
a certificate of an official veterinarian of the country of origin stating that they have inspected the animal and found it free from any communicable disease; and
a certificate of an official veterinarian of the United States stating that they have inspected the animal and found it free from any communicable disease and, if the animal has been quarantined or tested, the duration of the quarantine and the result of the test.
(3) A certificate referred to in paragraph (2)(b) may be accepted in lieu of the certificate referred to in subsection (1) with respect to any matter certified therein.
(4) A certificate referred to in subsection (1) shall not be accepted unless the official veterinarian who endorses the certificate certifies that it was issued by a licensed veterinarian in the United States.
(5) An equine, swine, bear, or non-domestic feline referred to in subsection 3.(1) that was born after its mother was inspected is not required to meet the requirements of this Document, as long as the animal is imported into Canada at the same time as its mother and, unless the animal was born en route to Canada, the animal is identified on the certificate, referred to in subsection 3.(1), of its mother.
Official veterinarian refers to a USDA APHIS Veterinary Services veterinarian. You would be best served if your regular veterinarian is also accredited. You have them fill out the form and the VS vet endorse it. Done. I used to handle imports/exports to Canada all the time. Canada is pretty easy. Section 1 is the applicable section. Section 2 is to prevent people from importing animals to the US and then just taking them across the border and taking disease with them.
Thailand....I can't find anything. Your best bet is to contact the Thai consulate unless your local VS office has tracked any info down. I used to also make the people who wanted me to ship their animal to an unusual country help, because of language and custom barriers.