I've been researching this same thing recently cause we're going through this with our own dog. I'm just about to the point of total frustration at the moment but not ready to give up. He's a big, 80-something-pound, lab-retriever-hound mix with a strong prey/chase drive. Started early teaching him all the usual commands - "no", "sit", "leave it" - he also generally responds to a finger snap & his name being called. Worked a lot with him on the leash since we often go to parks & take walks. Been consistent, & for the most part, fairly successful with all of it.
Had an incident not 2 days after we brought our first chicks home... That 1st day, we let him have a sniff around the box with the chicks in the house a few times & sit & watch, on his leash, box secured, my wife & I both supervising. He sat there staring for a good while, & I imagined that he was seeing those Bugs Bunny cartoon chickens that look like a walking meal.
We thought the best way would be to slowly introduce them & use the "no" command if he misbehaved... I had the chicks out in a temporary pen in the garden area (thought it was secure enough) while I worked on putting the finishing touches on the coop/tractor. Long story short, we lost one... to him. He pulled so hard on the leash that his collar broke & he had pulled up enough of the pen to get at them. Of course, he chased when they scattered. Happened in seconds.
They're in the tractor full-time now & we're still trying to get him used to the idea of having them around & sticking with the commands. Been working really hard on trying to curb that chasing thing. Took him out for a walk recently, he saw the chicks hopping around, & his ears went up. Gave him a firm "no". Totally failed to respond. Gave him another "no" & a gentle tug on the leash. He gave me the quickest glance. I had no chance to reward him for acknowledging me cause he immediately locked back on. I snapped my fingers, called his name, & tried to re-direct him by turning to walk in the other direction & holding firm to the leash. Before I knew it, he was lunging & pulling to get at them. I pulled the leash & ended up having to wrap my arms around him & pull him back. Grabbed the scruff of his neck, he laid down, & I yelled "NO!" & immediately walked him back in.
That was a couple of days ago. Didn't take him anywhere near that side of the house the next day. Took him out earlier today, he did perk up when he saw the chicks in the tractor, but he actually responded to my commands. Gave him a chest rub & told him "good boy" as soon as he looked back at me. After a moment, he seemed to lose interest & I walked him back in. Big improvement, but my question is still "what do you do about a trained dog that fails to respond to commands & completely tunes you out when he gets in that mode?"
I'm not really hoping to ever have them integrated. Just for the dog to leave the chicks alone & for them to be safe from him.
Not trying to hijack your thread, just sharing my experience. All I can suggest is do some basic training with your dog if you haven't already & work at that 'til you feel like you've both got it down. It'll take time. Then give introducing him to the chickens another shot when you think the time is right. It could take some time for that as well. It all might go away when the chicks are bigger. Might not.
In any case, you'll want to stop the running, lunging, & terrorizing behavior before it ever happens if at all possible. There should be some signs, like head and/or ears going up, a look of alertness... best to nip it then & not wait til it's already happening.