Most things are toxic if enough is eaten. It's mostly a question of 'are chickens likely to eat enough to hurt themselves'. For animals in general, and I would guess chickens as well but remember this is just guessing, marigolds and zinnias (and I *think* Thunbergia too) are among the safer plants. Personally I would not worry much about 'em.
For pets and livestock in general (I do not know whether there are any 'twists' to this that are poultry-specific), the things to worry most about (because they're toxic in lower amounts) are:
-plants with very strong toxins in them such that even just an experimental mouthful or two can be deadly (such as yew, oleander, water hemlock or poison hemlock [the latter two are queen-annes-lace type plants])
-plants with strong toxins concentrated in the seeds such that even just a seed or seedpod can be deadly (such as castor bean, daphne, laburnum, mistletoe)
-plants with a great deal of oxalic acid and similar compounds in the foliage (such as rhubarb leaves, Oxalis, daffodils, elephant ear [Colocasia])
You would probably also want to stay away from plants with large amounts of other toxins, such that you don't have to eat all *that* much to experience at least severe digestive upset, kidney failure, neurological problems etc (the other 'classic' poisonous garden plants, such as monkshood, foxglove, lantana, larkspur, etc).
Generally, the more of it an animal has to eat before getting poisoned, the less of a problem that plant is likely to be.
When livestock are poisoned by the less-hugely-deadly types of plants, it is almost always because they have not got much else to eat (picked-clean pastures without enough other food being provided). As long as animals have plenty else to eat, and you stay away from the 'kill ya fast' things, there will very seldom be any problems. Most poisonous plants are also nasty-tasting, and only the rarest of animals will just up and decide they're an obscure gourmet treat when other things are available
There are lots and lots of lists of the 'usual suspects' of poisonous garden plants available in books and the web (try google).
Hope this helps,
Pat