International import/export is tricky. You will have to check with not only US policies (if you plan on bringing him back to the US), but also Mexico's policies.
For going to Mexico
Check with them. Apparently they are not consistent, but you'll likely need not only a CITES but also your standard tests (like PBFD and others). It sounds like you'll also need some export/import permit, but this is not well documented, so do your research and go above and beyond.
For going back to the US
https://www.aphis.usda.gov/aphis/pet-travel/bring-pet-into-the-united-states/pet-birds/pet-birds-mexico
If I'm understanding correctly, this website says land travel is not allowed for birds. But here's what you would need to get back into the US:
21-day pre-export isolation, which is defined as:
- Pre- export isolation must:
- Occur for at least the 21 days immediately preceding the date of travel to the U.S.
- Be supervised by an official government veterinarian, or by a veterinarian in the country from which your bird is arriving who issues the export health certificate and has been authorized by the foreign government to supervise the quarantine.
NOTE: This isolation can be accomplished in the home so long as it is under the approval of the veterinarian who will issue the health certificate. There can be no other birds in the home (unless they are being shipped and are listed on the import permit).
- Once pre-export isolation has been completed, the pet bird must be transferred directly from the isolation location to the port of embarkation (airport) in a carrier that has had seals applied by the government veterinarian.
- The seals must have identifying marks or numbers which are then recorded on the health certificate.
- appropriate U.S. Fish and Wildlife Service (FWS) certifications and permits;
- a Veterinary Services (VS) import permit.
- an original health certificate issued or endorsed by the government of Mexico
- upon entry in the U.S., disease testing and a 30 day quarantine
If I recall correctly, if you can prove your bird is US-origin (microchip or closed leg band with records), then the 30-day quarantine could be done at home rather than the standard federal facility... Don't quote me on this.
So do note that it's 21-day quarantine in Mexico plus 30-day quarantine in the US.
I believe Amazons are legal in all US states, so that's fine going across state borders, if that's any consolation.
Long story short, TBH, from my narrow perspective, it doesn't seem worth it.
I live in a country where if I do want to go on holiday, I have to go internationally (yay, city-state country). And yeah, I'd love to take our little guy with us, but it's too much of a risk and it's too expensive and it's way too time-consuming. It honestly would be more stressful than leaving him home.
I'd recommend looking into having a friend house-sit/pet-sit at the same time or find a parrot boarding place you trust, even if you have to drive quite a distance to that boarding place.