I think they do. My cockatoo absolutely does. He will actually say words when he wants things, or is unhappy etc.
Chickens now, I think they do, in their own language, if you take the time to stop and listen to them, don't just hear them, LISTEN to them, they often are telling you things. I can tell when they want snacks, or if the water is low in their coop or something has them not happy, they'll come tell me. Sometimes they'll stand around or go over by where the problem is to try to tell you.
I had one of my dum dums get herself in the hav a hart trap and locked herself in the possum trap (don't ask) Well her sister, was all whiney and moaning, and I was asking her what's wrong, long drawn out bwaaaaaaaakkkkkkkkk like they do when they are vocalizing. She's standing behind the coop looking at me, looking over behind her, behind the coop, at me, back. I say what's wrong sweetie? and start walking over there, she immediately jumps behind the coop. As I get around the corner she's standing on the cage, vocalizing, shes upset... it is THEN I see the little one INSIDE the cage. So yes I firmly believe some can talk. One comes up to me and wants me to pet her or does the submit and Ill ruffle her up telling her how pretty she is, and she's all happy and will have a brief conversation, which I am pretty sure is. ok so now where is my treat.
The other day midnight got into my strawberries and tore them up. I grabbed her and held her at eye height and very sternly told her, what the hell is wrong with you !! WHY DO YOU KEEP GOING INTO THE STRAWBERRIES !!! Giving her an angry look. She held her head down, looking down, she'd occasionally look up, like eyes looking up at me and I swear to god, if I chicken could have a guilty look on it's face SHE HAD IT. It was like a feathered puppy when you scolded it.
Then I got another one who is dumb as a stump and im surprised doesn't drown by looking up when it rains...
Yes, they absolutely DO speak with us. We just need to take the time to learn, recognize and understand the language they are speaking though.
Aaron