I've linked to another recent thread on this topic, and will move this thread to the Home and Environmental hazards forum area too.
https://theparrotclub.co.uk/community/index.php?threads/safe-cookware.29096/
Many sites quote the risk factor as being when Teflon is burnt as it is the high temperatures that release the fluorine...however this is NOT the full picture, and if the non-stick (PTFE) coating is damaged in any way - scratches, chip, etc then breakdown of the chemical coating can occur at lower temperatures too.
One of the worst culprits is the non-stick oven liners sold by kitchen shops such as Lakeland and some of the door to door catalogue people...this is a complete NO NO if you have birds...and if you have heating elements in the bottom of your ovens you should not use this product at all, I had an elderly neighbour who did, as there wasn't a warning on the product she bought, and she used it in her main oven which had both top and bottom heating elements...she noticed a smell, and started to get a headache...so quickly opened all doors and windows and turned the oven off, and won't use again...headache and sickness for humans, far worse a reaction in birds.
Check the info provided with your non-stick items if they do not state PTFE free (and don't get that confused with PFOA free) then don't purchase....some don't say...like the OXO baking tins ...but if you google the brand name of the particular non-stick coating you can usually trace, as they all originate from a small no of manufacturers...if in doubt post here on forum and we will help you.
Ceramic coatings are usually OK, Pyrex, stainless steel etc.