Best blood clotting agent EVER: Clotisol. You'll have to buy it online. It's what exotic avian vets use for parrots, including in-beak injuries. A small bottle will last you ages and ages. If it dries, you add clean water to reconstitute it.
Trust me - it STOPS bleeding, even heavy bleeding, stops it immediately. We had to use this on a cockatoo who was a mutilator.
Other things:
nylon gloves
cuticle scissors (great for trimming around wounds)
A large pair of Penny-cutting scissors (great not only for trimming large feathers, but also for bandage cutting as they're not sharp)
regular gauze pads and wraps
Hydrogen peroxide
Betadine
VetWrap or similar self-adhesive bandage - at least four things of it. (Keep the tubes - they make good splints)
2 20-30 cc syringes without needles (for flushing wounds)
a couple of 3 cc syringes with 12-22 gauge 3/4-1 inch needles
a bottle of Procaine G Penicillin (fridge section of feedstores - keep in fridge)
popsicle sticks, paint stirring sticks (great for making splints; popsicle sticks are awesome for putting antibiotic ointment on wounds)
Duct tape (very useful for binding bandages using tiny strips of it - it does NOT come off)
a clean white cheap sheet (great for making splints, bindings, cover for wounds, etc)
paper towels
suture material and attached needle. Order online, the size for cats. You'll never know when you might need it.
tweezers that stay in your chicken med box.
SWAT brand antibiotic ointment (horse section, feedstores, contains fly repellent to prevent maggots in wounds)
Neosporin tubes - two of them. One to contaminate, one to use generally.
Q-tips
Nitrofurazone ointment (also horse section, feedstore) is a great healing ointment as well.
Dusting powder for lice, or sevin dust
Probiotics (kept in fridge - yogurt, probios, acidophilus tablets, fastrak, etc)
Oatmeal (for grinding and making oat-water for birds reluctant to eat)
Pedialyte (for electrolytes)
A small bottle of wheat germ oil (for building up a sick bird)
Sulmet and/or Corid.