i think chickns can learn simple things, my chickens know that when i come the get food and something yummy to eat, so they come running/flying and stay all under my feet till they get something. on the other hand they know my father in law but he dont feed them and dont spend time with them, so when he comes the run away from him.
But i also think that chickens cant think things for themselves and figure out thing. for example, 3 times the same chicken flew out of the coop, i watched her for a minute and i saw she had no idea how she got out, and no idea how to go back in. she would stand by the chicken wire and look inside, but she didnt try flying back in, just kinda packed on the wire trying to just get in.
you can train any animal to do something in order to get food.. like they trained rats to push a button if they want food, on a psychology study. but not any animal can figure out things. in a different study they put a monkey in a cage with 2 different size sticks and trew a banana outside. first the monkey tried to get it with his hand, it was too far. and then he figured out he can use one of the sticks and thats what he did.