By googling "PTFE toxicity to birds" you will get a good number of hits. There seems to be a consensus about the lethality. As in, get those PTFE coated pans out of your house if you love your birds!
When PTFE is heated, or worse, over heated, it will produce toxic fumes. It seems the higher the heat, the more and worse the fumes. The reason for this toxicity for birds have an high efficiency of their respiratory systems. That also means they are more susceptible to airborne toxins. This does not mean it does not impact humans; it does, just not as much.
In people, the disease has flu-like symptoms and is known as "polymer
The best piece I could find on PTFE toxicity was this report on Polytetrafluoroethylene Toxicosis in Recently Hatched Chickens.
What is bird safe cooking ware?
Remove all Teflon / Non-stick Coating! Period.
Stay with stainless steel and cast iron stuff. Do research on your food prep setup. Find out what that non-sticky layer is made of.