Ya know, Its funny you say that because when the flowers fall over the fence into the yard I'll often find little peck bites out of the flowers and have never seen the chickens sick, I am very diligent about making sure I chuck the flowers back over the fence because I don't need little saplings...
I have had the hardest time with an extremely invasive plant in my yard, I dug up the whole root system this past spring and it still pops up everywhere. Trumpet Vine or trumpet flower is poisonous, and itchy, for all animals and humans, and yes my chickens. The original plant is in my neighbors...