when we got our tiel we went out and got a stainless steel fry pan to be on the safe side..
but my parrot breeder friend in the USA says her parrot room is right next to her kitchen, with nothing but a screen between. She breeds parrots worth thousands of dollars and still cooks with Teflon coated pans. She said she you ahev to really burn the pan before it;s dangerous and has never lost a bird yet from teflon fumes.
I use other cooking equipment with teflon.. sandwich grill, waffle maker etc and it's fine . Just anything new I open up the windows really well and heat up the item quite hot to let any residue evaporate .. that new smell you get with most cooking things.