A) I would be concerned about the spiciness of kimchi. Some animals, dogs, cannot handle the spice of peppers. Kimchi is made with hot red pepper powder. Cayenne pepper will kill a cat. Cats will eat it because they do not have the taste-buds for spicy-hot.
B) the probiotics in kimchi are in other fermented foods -- including dill pickles -- fermented pickles, not the "pickled-in-vinegar" pickles. As has already been mentioned, sauerkraut is another option. It is kimchi without the fish and spices.
C) if you really want to do the probiotics-for-my-chickens thing try putting some kombucha in their drinking water. Actually, I have thinking about doing this myself. You can make your own kombucha. The starter culture is available from:
http://www.culturesforhealth.com/
They have everything anyone needs for fermenting -- including recipes for sauerkraut ... that you can feed to your chickens.
D) back to kimchi -- I can certainly attest to the very high quality of this recipe:
http://www.maangchi.com/recipe/tongbaechu-kimchi
I always have this kimchi and Maangchi's recipe for radish kimchi in the fridge. But like I said, I would not feed it to chickens. My chickens sometimes get into my garden. They never touch the nightshade plants (tomato, potato, eggplant, peppers (sweet and hot)). There is something in nature that tells the chickens to avoid peppers ... and they do.
Give them sour milk (which, like yogurt, is full of natural pro-biotics) and they will lap it up like it was ambrosia.
