We are both chicken and dog people and I think the uncle is way out of line. I know some people don't think of chickens as a big deal -"what's one or two, more or less", but if you love them like pets, you don't feel that they are just barnyard animals. And I also don't approve of beating a dog. First of all, it doesn't work. A dog who is scared of its owner still doesn't understand what the rules are.You have to teach them what they are and are not to do. I don't think this uncle will be inclined to spend much time on this, so it's up to you.
This might be more difficult, since it's not your dog and you probably don't like him much right now, but it can work. This is what happened with us. My significant other's dad had a German Shepard/Collie mix who was a confirmed chicken killer. Every time he got away, he ran down the road to the neighbor's chickens (free range) and killed all he could get his mouth on. We inherited this dog when his master died 18 months ago and we already had chickens at the time. We weren't sure we would be able to keep him because of his history, but we decided to try to work with him and to see how it went. We started off with him on leash, outside the chicken pen. Every time he panted or drooled or focused too hard on the chicks, we corrected him; not by beating him but by speaking sharply and giving the leash a quick jerk to redirect him. Then lots of praise and patting when he relaxed and focused elsewhere.
When he was good outside the pen, we moved on to leashed with the chickens. You have to focus completely during this lesson, because dogs are quick! We let him get a little close, but always had complete control over the distance between him and the chicks. Again, correction if he made a mistake and lots of praise when he did well. When we felt comfortable, we let him off the leash, but followed him around the yard using sharp voice commands if he seemed too interested in the chicks. Now we can let him loose in the yard unattended. This didn't happen overnight; it took 2 or 3 weeks of almost daily lessons. And now he is so much happier and calmer inside the yard and out.
I know this is quite a commitment on your part, but you will be so much happier if you can live in better harmony with your dog neighbor and not have to constantly fear for your chickens safety. Good luck with whatever you decide to do. I hope you can get to a place where you can enjoy your chicks and they can enjoy their good life with you!