Here is my list...
For wound care: Chlorhexidine, plain triple antibiotic ointment, Vetericyn, large syringes for flushing, 4x4 gauze pads, 2x2 gauze pads, vet wrap, gloves.
For eyes: Saline solution, Terramycin, small syringes for flushing.
For supportive care: 14/16 and 18 French feeding tubes, large cath tip syringes, materials for a sling, a kitchen scale, old towels, puppy pads.
Illness (May expire - use your own judgement here): Baytril, Fish Mox, Vitamin B Complex, Nutri-Drench, Vitamin E capsules, Calcium Citrate tabs, Corrid or Baycox, Ivermectin and Praziquantel de-wormer, permethrin based spray for external parasites.
A small (or medium for LF) folding dog crate is also a must have for isolating sick or injured birds.
For electrolytes, I use Pedialyte, which is easy enough to grab in a pinch.
ETA: Totally forgot tools. A pair of blunt ended scissors and a pair of sharp scissors, tweezers, and I keep two pairs of hemostats. A curved pair and a straight pair.