I don't think you have a clear understanding of why your dog is killing them. Your dog is hunting them and gets a lot of pleasure (reward) while doing it. The dog will not associate a dead chicken with the living chicken they are hunting or just hunted. You are dealing with two completely different motivations with the chicken on the fence scenario--one is prey drive (hunting) and the other (sniffing the dead chicken) is curiosity or just plain hunger--very different motivations.
If aversives are going to work, the punishment has to be applied as soon as the dog goes into hunting mode. The timing is critical. You need to make it so bad they never want to do it again. The most effective use of punishments is when they are really bad and used just once. Think about a child learning not to touch a hot stove. Certain temperaments and breeds of dogs won't care how much you punish/abuse them--they will ALWAYS follow their instincts.
The only thing I have had longer than horses is Dogs. which is all my life 58 years. I have seen it all from Drop kicking the dog out the back door.... "dads solution" to wheedling and cooing at the dog to stop .... "moms solution" Neither has any effect but to make the owner feel good.
My last dog lived 19 years. A mutt from the pound with some Greyhound and Aussie mixed in. this dog had a very strong prey drive with an added bit of herding to boot. Before I got chickens I had her and I taught her a command which was essentailly .... "no Dogs" It could mean no dogs touch my plate when I leave it on the floor..... No dogs to get out of the car.... meaning I could leave the window open and she would not jump out. I would test her periodically but NEVER put her in a situation where the temptation would out weigh the conditioning. Soo not fair to the dog.
When I introduced her to chickens it was through the brooder cage. She would sit and vibrate with excitement.... as soon as I saw that I said.... "no dogs" and left her alone to figure it out. Meaning I was there but not picking at her over it. She would calm then but continue watching the chicks.
One got out and she immediately went to it but when i saw she was watching but not acting on her prey drive I told her she was a "good girl" I caught the chick and in the process was able to observe if she got excited over that.... all good. If I had known how to train it I would have loved to work with her herding skills.
To that effect enter four Goats..... Terrified of dogs as I find out. So I had the opportunity to work with her a bit.... The goats got out of the yard and were being ****holes to herd. So I Told Rosie.... Go around and pointed with an arc. I will be darned... she did it. She went out and around the goats and off they went into the safety of their pen.
I think too often people try to make a dog fit in their niche rather than choosing a dog that fits. I got lucky with Rosie and would clone her if I could. For instance I am a Greyhound person Love em to death and when I have yards that are secure I iwll have them again. I will be under no dilusions that I could train a greyhound to be chicken safe..... or cat safe.... ever. If it runs or flies their brain goes in to heat seeker mode. There are Sooo many breeds that the pray drive is very strong with.... Terriers, Hounds, Dogs with close wolf ancestry as well.
Some dogs will surprise you though. Rottweilers well bred ones and Poodles, both were used as an all purpose dog, Hunting herding retrieving.... Rotties were originally bred to work the stock yards.
There are always exceptions to any "rule" .... sigh I am rambling again.
I have to go order hay to be delivered before the wind starts up...
deb