As First Responders, you may be fully trained for disaster response for human lives and property. Rescuing wild psittacines is another universe--the basic principles apply but the victims are very different.
The best preparation for psittacine victims is to make contact with local wildlife carers or rescue organizations, in advance, which even in non-crisis times is valuable and mutually beneficial. They may need your assistance on many levels, even in normal times (and vice versa). Join training, drill and exercises can be valuable.
It is very important to be familiar with the laws governing wildlife interactions within the country. In some areas, even benign assistance to injured psittacines may be an actionable offense. Making friends and securing professional bridges with local wildlife authorities will go a long way in the event of a catastrophe.
Gaining experience with psittacine restraint, capture, examination, and care could mean life-or-death in the field. It is well worth finding wildlife rehabilitators, avian-experienced veterinarians, and and others willing to train you on these skills.