Most airlines allow only one cat per person, a few allow two in the same kennel, but they are exceptions to the rule. details
https://www.travelingwithyourcat.com/can-you-put-two-cats-in-one-carrier-on-a-plane
Southwest allows 2 in the same kennel, but only domestically. American Airlines supposedly allows 2. However, visiting AA, only one ESA (Emotional Support Animal) is allowed?
See also: https://www.shermanstravel.com/advice/carry-on-pet-policy-by-airline-the-full-rundown

On American Airlines, the kennel replaces the carry-on bag, so depending on the airline, you may be checking in a bag.

ESAs (emotional support animals) used to travel for free with their owner. Due to lobbying by the airline industry, legislation has changed in USA regarding ESAs, starting Jan 11th 2021. Now only service animals can travel for free, and only dogs qualify as service animals. Changes in policy in USA seems to affect the rest of the world, much like Europe's GDPR changed website policy globally. Although there are some exceptions as each airline and each country can make its own policy.

Most airlines charge a fee for traveling with a pet that is not a service animal, and the fee is astronomical; around $200.

LATAM airlines states that cats are allowed to travel for free as ESA (emotional support animals), but only routes from or to Mexico and Colombia, and on domestic flights within Colombia. The weight of regular **non-ESA“* pets traveling in the cabin must be less than 15 lbs (7kg) INCLUDING THE CARRIER.

For other airlines, the check the link left in the discussion section by some stranger and/or esadoctors.com. Do check with the airline for latest policy.

Lima <-> Chiclayo

In your country of residence, your vet can certify that your pet meets the requirements of the country you plan to ingress. The certification process may involve taking document from the vet to a government agency for an official stamp.

USA: https://www.aphis.usda.gov/aphis/pet-travel
Uruguay: https://www.gub.uy/tramites/solicitud-egreso-mascotas-uruguay, and more specifically https://www.gub.uy/ministerio-ganaderia-agricultura-pesca/politicas-y-gestion/informacion-para-personas-viajan-mascotas

The requirements may be very stringent. Start early!

More about vaccinations...

I've read to fast the cat for 6 hours before travel. Not with my cat! Nothing in the morning, no matter how much she begs. Drueling, throwing up, and diarrhea will result.

https://www.wwwallaboutcats.com/best-cat-tracker

You can also use smarttags from samsung or airtags from apple. Smart tags depend in part on a network of apple or samsung phones reporting the tag's location. For the purpose of backpacking in the wilderness, RF tags give better range. “The advantage of RF is that this technology has a wider signal range, which can be up to 30 yards. RF can go through walls and there is no need to point the remote to the device, as it does not require to be in line-of-sight.” Compare that with 30 feet for bluetooth. Tabcat / Loc8tor tags also start beeping when you are actively looking for your pet.

About airtag direction finding: https://www.reddit.com/r/iphone/comments/mvbm6f/how_do_iphone_know_the_direction_of_airtag

Microchipping may help you recover your lost cat, but only in certain countries, and only where they use scanners compatible with the cat's microchip:
https://en.wikipedia.org/wiki/Microchip_implant_(animal)#Cross-compatibility_and_standards_issues

Some “natural” products, such as apple cider vinegar ¹⁾, and aloe vera with abscorbic and citric acid (citation needed). Essential oils can be toxic to cats, so check ingredients on any store bought insect repellent.

Picaridin, applied to humans, does not seem to be toxic to cats, but long term research has not been conducted, and other ingrediens in the repellent need to be checked. NPIC fact sheet

Permethrin is very toxic to cats, but may be used by applying to clothing and letting dry in an area away from felines. However, permethrin would not be recommended if your cat sucks or chews on your clothing.

Some flea topicals for cats, such as Revolution, will also kill mosquitoes.