In Oregon, trumpet vines are very invasive. And they have invaded. My 4 to 12 week chicks ate them to the ground this spring and didn't seem to have any issues. They eat grape leaves all season and grapes when they are ripe. As well as also invasive Himalayan blackberries. The only thing green left in their current pasture (we have NO rain from the end of June through the middle of October) is English ivy and some weed I can't name. They may have tasted it the first day they were in this area, but it's all still there, untouched and the rest of the area is dirt. They do seem to know what's not good for them.
Sunflowers are great. I plant them really heavily from a bag of black oil seeds. I thin the new plants and tie the stalks to the fence. Chickies love the leaves and in the fall I save the seeds to feed them for the rest of the year.
My dog also very gently picks blackberries (only the ripe ones) and eats them. He will also pick apples from the low branches. He ate a bunch of plums that fell this year - that was one big mess to clean up the next morning - and darned if he didn't find a few more the next day. So far he hasn't touched the grapes, though they are on the other side of the fence.