The parts in your screenshot are talking about cancer risk, not about what fumes it gives off when overheated.
Yes, it's fine under normal circumstances. If it's not getting too hot, it's safe for your cockatiel, the OP's chicks, and everyone else too.
Heating it too hot is when it gives problems (someone sets a pan to preheat and then forgets about it, or they're cooking something and forget to turn off the pan so it boils dry and gets really hot, or something like that.) It's the kind of mistake that's fairly easy to make, but also fairly easy to avoid.
For example, here's a page on the actual Teflon website:
https://www.teflon.com/en/consumers/teflon-coatings-cookware-bakeware/safety/bird-safety
It warns to keep birds out of the kitchen, not leave cookware unattended, not let it get too hot, and use windows or an exhaust fan when cooking.
And here's a page from a website about parrots:
https://www.allaboutparrots.com/cookware-parrot-safe/
(Summary: they recommend that all parrot owners avoid all the common Teflon and other brands of non-stick cookware, because they think that's safer than trying to be careful not to overheat it. But they do acknowledge that keeping it within a safe range works too.)
Statement of the obvious: a google search yields lots of results on all sides of most questions. In this case, my searches mostly turned up two categories of results: "eating the food won't give you cancer" and "fumes dangerous to birds."
I'm not trying to say that every use of a non-stick pan will kill birds.
I do think it's one (of many) causes that is worth looking into when someone's birds (including chicks) die unexpectedly.
And I do think that being extra-careful not to overheat pans, or to temporarily use other pans, might be reasonable if someone's brooding young chicks in the house. (Depends on the individual person-- how much they worry, and how attentive they are to what they're cooking.)
