I would not say that it is safe. This is because a process of dihydroxylation and sintering occurs in the paint when it is baked. Additionally, paints contain various types of toxic metals that can be released into the air when heated and baked. This isn't good for any living animal but especially not birds.
That being said, you could paint them outside and bake them later on at a friend's or other family member's house. After being washed they'd be safe to bring home.