it's actually pretty easy to train a dog to be good with other animals. Main thing, though, is to get them off the chain and into the family!
exercise every day - and that means you out there with them, not just putting the dogs in the yard and expecting them to entertain themselves. take the kids and the dogs on a walk. buy a chuck-it and play fetch. get the kids involved in helping with training - they can help teach the dogs to sit and lay down if they are old enough.
My boy Rayden was raw-fed for most of his life. One of his favorite foods was rabbit and there isn't a wild bunny that is safe from him though he's too old to catch them now. But, I can tell you that he knows the difference between rabbits that are family and those that are food.
You already know that he is excited with the chicks. Find the closest distance that the dog first notices the birds in the brooder. This might be in another room if he is one to constantly glance at the door. Put your dog on leash and get some extra special treats that he only gets for this work - bacon, grilled chicken (no spices!), hot dog chunks, etc. When the dog glances toward the birds, say his name and "leave it" If he looks at you, give him a treat - if he doesn't, give a light pop on the leash (think tap on the shoulder). When he looks at you reward him.
You can also teach him "watch me" the same way. You can practice this at random times though out the day. If you have a couple extra minutes while you're watching TV or whatever, just say his name, pause, "watch me" When he makes eye contact, then reward him. You can also (if you get in the habit of keeping a small treat in your pockets) catch him looking towards you say "watch me" and then reward. Or just praise him verbally.
Once the dog is reliably paying attention to you and the birds at a distance, move a little bit closer. If he absolutely blows you off, you're too close. Just back up a bit and begin again. Eventually you will be right amongst the birds. You can then start at a distance or with a long line (20' leash or so) and work from there. I never ever leave my dogs/chickens loose unattended together.
I don't even trust Rayden
I don't mean I constantly hover over the dogs when they are out with the birds, but I am in the area and aware of what they are doing. Think of it as a small child. Even though you've taught them not to play with matches, would you leave them alone in the house with matches scattered all over the floor?
The most important part of the training is to set the dog up to succeed. Don't give him a chance to chase the birds. Don't give him a chance to disobey.
Yes, it takes time. If the dogs get along well together, you can cut down on the time by exercising them all at once. Use the chuck-it and several tennis balls to get the dogs racing all over the yard. Add in some obedience by having them sit before you throw the ball. You'll be amazed at how quickly they catch on. Do an hour every other day and you'll be amazed at the difference.
For the training, I'd set aside 15-20 minutes a day per dog. Less would be better than more, so if you only have 5-10 minutes per dog you can still train them easily.
Honestly, that amount of time is the LEAST that you can put into a dog. It's a basic need, just as important as food, water, and air. That is also why many states are moving to make it illegal to chain dogs all day. Out for a potty break or some fresh air is one thing, but to live 24/7 that way is torture.
ETA: The best thing about teaching "leave it" is that it works for everything. Drop something on the floor and don't want the dogs to touch it? "leave it" See dog running toward a snake? "leave it" Lots of training and work, but it pays off!
Of course, some dogs just can't be trusted off-leash. Period. They are just too focused on the birds. In that case, just confine the dog when the birds are out.
