All I know is that you can eat the sprouts and the leaves have traditionally been used for tea. I'm not aware of any problem with eating the mature leaves. They aren't traditionally eaten that way, but that may have more to do with taste or texture of the mature leaves. You could always let the plants go to seed, since the seeds are such a powerhouse of nutrition.
Tomato plant foliage develops toxins when they're more mature and fruiting. Most plant foliage that I know of is usually either toxic or non-toxic, though. With the absence of any data on toxicity anywhere, plus the history of mature leaves being used for tea and the young sprout leaves being eaten, I think they are probably safe for your chickens to eat.