In the meantime, start teaching that dog something like "leave it" as a command, so you have a way of telling the dog that the chickens are off limits. Does it fetch? Using a toy to teach "leave it" is the easiest, or you can teach it kind of as a No! command whenever the dog gets into mischief. Or have one command for "leave it" and I also teach "enough!", which means stop what you are doing as opposed to drop that. If you can't get his attention with your voice put him on a leash to teach this. I don't give treats for these things, I just expect them to do what I say and then enforce it. But some people teach leave it by trading up, giving a treat for when they release the object. But it would be a really good thing to work on prior to getting chickens. I have no idea how to teach dogs to herd however so don't ask me about that, other people on here are probably better at that.
We found with our dogs, at first they seemed waaaaay too interested and we kept them 100 percent apart. Then over time we saw that most of them lost interest in them, especially when they saw them every day between the rungs of the fence. They are more interested in eating that yummy chicken poo.
When they "met" again, the dogs had no reaction, the chickens did not run.....except ONE of our dogs, she is the one who would chase/kill/eat them. She is a more primitive breed. So we don't actually let her into that yard, in my case, I have a large pen without a top (too large) so the chickens sometimes fly over, so she cannot be trusted back there, and I let her have potty breaks in my front yard only. But she is older and probably harder to train because of breed, and I don't try to make her change her instincts, I only try to manage the space to keep the chickens safe. Between THAT dog and the chickens, I try to keep two barriers. Meaning like a fence and a door, or two doors, or a crate inside a room and then a door blocking her from them as well. Too many times she has been able to outsmart us and escape and she killed TWO of my chickens. The first one was the dogs fault and the second one was my fault because I should have known the dog would do it again. But we have had about a year go by now without another accident since I started managing this dog differently and keeping two barriers between. You could learn from my mistakes. I just assume she will kill and eat them so she isn't allowed anywhere near them nor allowed to run free. We have neighbors with chickens as well so running free is just not an option for this dog.
If you just want eggs for family use, three hens is really pretty good, unless you have a big family or eat a lot of eggs, that should give you over a dozen a week. Chickens will pick over the foliage in your yard and kill it off especially if the ratio of chicken-to-yard is such that they eat up what is there too fast. You could always add more later. They are like potato chips you know, but it is much easier to keep the space for three chickens clean and non-smelly if your space is limited than if you started adding.
