Sure the easy and obvious solution is to eat them. But if you want to keep a stubborn goat around, here is what I do that seems to work.
First, I have bottle raised goats and only have experience from that point of view. I have heard a dam raised goat is more "wild". So, good luck and it might take longer to get them tamed down. Just guessing.
Some of this is how I would milk any goat and will address kickieness as I go along.
I get the goat out of the pen, calling her by name. Let's use Angel as our "test" goat here. Since she is thee kickyest goat I have ever owned. I knew I was headed for trouble with her when she was still pregnant and would sit/lay down on the milking stand while I was trimming her hooves. My husband and I dragged her onto the milk stand twice a day, every day, for a week before she started jumping up by herself and it took 2 weeks total before I could trust her to get up there without needing the brute strength of my dear husband. This was all while she was still pregnant.
I had a 30 year goat veteran tell me that they wait till the goat kids and put her on the stand right away and don't mess around with training them to get on the stand prior to kidding. Of course that was after we wrestled a Angel for two weeks. Oye.
So, I have Angel out of the pen and she willing runs and jumps up on the stand. I put her head in the stanchion and lock it into place.
(insert pic of Angel on the milk stand locked into place prior to grain)
Since I have worked with Angel awhile now I do give her grain right away now. When she was very kicky I gave her grain after I brushed her and washed her udder. I was udders with a 1/2 a paper towel or a single select a size sheet. I have a few drops Shaklee Basic G of in a spray bottle of water. Some people find this is drying to the udder and so they use Shaklee H2 instead. I spray half the piece of paper towel with this, wipe the udder, turn to the dry half and dry the udder. If dirty I repeat.
(picture of spray bottle and paper towel)
I have already given her, her grain ration (about 4 lbs of grain), but if you have an extra kicky goat then you will give her grain at this point.
I sit down next her facing her rear, not facing her. I lean my shoulder into her side and reach up under her with my right hand as my right side is against her right side at this point.
Oh wait lets go back a bit. My milking stand is up against a wall. Then I can push her against the wall when she gets too wild. I have found my kicky goats like to be against the wall anyway. I tried flipping things around in my goat barn once and they freaked out. I had changed it so I was on their left and I had my left side against them. They all kicked and kicked. And I had trouble getting a grip on the Udder, since I am right handed its easier for me to reach under the goat with my right hand. I quickly switched it back. So, maybe address those issues in your milking set up. See if your kicky goat just wants to be milked from the other side, or with you leaning against her. Up against a wall or away from a wall. If you have a goat that was milked by someone else before you ask them what their milking area is set up like and what not that goat might just want what its used to. Did they hand milk or machine milk? Some goats are stubborn as, well, a goat!
So address those issues and come back, um Kay?
Glad to have you back. grin.
OK, so where were we?
Angel is on the milking stand. Happily eating her grain. I am sitting down facing her rear. Our right sides are touching with my shoulder leaning against her right side. I reach under her belly to her left udder with my right hand, left hand on right udder. I milk her.
Stubborn goat lifts her left hoof HIGH off the stand. I felt her lean towards me readying her self to lift a leg, so I pulled the bucket with my left hand towards me (away from her lifted/kicky leg). I used my right hand to grab her left hoof and pull it back down to the miking stand and hold it there about a half minute, while I resume milking one handed, using my left hand to milk and my right hand to hold down the offending leg. If it was her right leg I would grab it with my left hand and milk with my right. All in one sweep. I also loudly and sternly say, "Angel NO! Stand good." I release her leg after she has settle down and relaxed. In this case about a half a minute. I slowly release it, ready to grip it again if she shifts her weight like she is going to lift it again.
I have got her teat before and grabbed her leg and took her teat with it. That can't feel good to her. I wonder if that is the main reason she has decided to kick less...hm. So, if all else fails grip a teat and a leg and pull down. (insert evil laugh here)
I also take two stainless steel milk buckets out to milk my four goats. I put 1 frozen water bottle in each bucket to get the milk cooling right away. If you have a really kicky goat I suggest having 1 small bucket you can milk into and dump into the larger bucket(s) periodically. So you don't lose all the milk if she succeeds in getting her hove in the bucket. Or on the edge of the bucket and tips it. I would MUCH rather have a hoof in the bucket and have to dump milk than to have the bucket flip over and spill it everywhere. Easier clean up.
Angel is doing MUCH better. Meaning she lifts a leg up or kicks 2 or three times during our 10 minute milking session, verses 10 or more times. She also does not squat down on the bucket like she did a couple times before.
For squatting on the bucket I jam my shoulder up under her and lift up and tell her, "NO, Angel Stand good." I have been told you can put a bucket or stool or something under their belly, for really stubborn squatters. But she is the only squatter I have had and she does it very rarely.
My first two goats were kickers as well. For them tying them to the goat stand worked. So, I tried this with Angel, once. That was all I needed to know it was a very bad idea.
I tied bailing twine to the leg that she kicked with most often and tied it to the leg of the milking stand. tight enough that I thought she would not be able to lift her leg. She promptly backed up and created some slack and lifted her leg! Then she leaned forward and mule kicked, lots. End of experiment with tieing down her leg. Angel then thought, "That'll learn ya! Don't tie me down!"