I honestly don't know because I didn't paint it.
Let's face it, paint is the least of their problems!
In the short time I've had hens, 3 were killed by foxes, 1 chick was squashed by a hen while hatching, 1 pullet died of unknown digestive abnormality, 2 hens died of reproductive health disorders. 1 hen (the chick murderer) is living with hepatic lipidosis, 1 hen had a hernia (which was surgically repaired) and now has an eye injury, 1 hen is living with a chronic and seemingly incommunicable bacterial infection (the working hypothesis has two parts (1) the environment is too dry for bacteria to thrive once she sneezes them out - it is quite a dry, sandy environment and (2) the hens are not at all crowded; and it seems likely that studies of communicable bacterial infection were conducted in crowded, possibly humid environments).
As far as I can tell, not one hen has tried eating paint and become sick from it, or become sick from eating anything in the proximity of the paint.
Maybe the ladies who painted it for me used special chicken coop paint?
Edit! We recently used water based exterior paint on the new roosting box! (We'll just pretend my memory isn't failing

)