Modern paints are safe once cured. That is they don't emit fumes and aren't harmful to ingest. I don't recommend eating the paint off of the walls. Not all paints are safe to use on surfaces intended for the preparation of food, because of the chopping, cutting, or acidic actions might contaminate the food.
My coop is painted on the inside. The birds don't peck the paint off of the wood. On the outside, they peck bugs and other things off of the painted walls, but don't take the paint off.
With millions of children in the United States chewing on furniture, toys, and woodwork; harmful paint would be the bane of our existence. This is why there is so much emphasis on detecting and managing lead-based paints used prior to the 1970s, before they were banned.
If you have flaking paint, you might want to take care of that. Since the flakes will fall off or come off easily, there might be a problem with the birds eating some of it. It should not hurt them, if free from lead.
Properly applied paint works well for my birds.
Chris