I just happened to see this post, and I totally agree with Sailboat, as any type of fumes like this are extremely scary and dangerous for your birds, however, if you yourself can actually still smell the coating burning-off, then if your birds are inside of your house, then they are breathing those fumes in all day long, for at least as long as you can smell it. This is extremely dangerous for your birds, and frightening to be honest with you.
Having your bird(s) by an open door or window is not good enough, as they are still going to be breathing those fumes in. If you can still smell the coating burning-off as of today, you need to get your bird(s) out of that house and let them stay somewhere else until you can no longer smell the coating burning-off, and then if it were me, I'd keep them out of the house for a week after you can no longer smell it, with the house airing-out as much as you can possibly let it by opening windows, doors, etc. Keep in-mind that just because you can no longer smell the fumes doesn't mean they aren't there, and for birds this is extremely dangerous and potentially fatal...
Do you have a relative or friend who could keep your bird for a week or so? The nice thing about birds is all you have to do is take their cage over to the person's house, and all they have to do is make sure that they have fresh food and water every day, it's not like watching a dog who needs to be walked, will go all over the house, etc. And if not a relative or friend, is there a Veterinarian Office or pet shop that you can board him with?
It's just not worth the risk at all...