I've been giving Penny a 'dob' of goat milk kefir with each meal lately, in an effort to improve her gut health and thus her immune system.
So far there are no problems, even though I accidentally dropped in more than a 'dob' yesterday.
Two of the humans in our household drink kefir ourselves every day (home made, a very easy process) and feel it's doing us good, but we wouldn't have given it to Penny without the say-so of a canine specialist. However, when I saw it at the canine naturopath's shop I trusted her to have researched it well.
This article is one of many online promoting the benefits of kefir for dogs.
However, this article suggests water kefir may be better than dairy kefir. I haven't tried making that myself, and the naturopath doesn't sell it, so that may be something to look into in the future.
I'm interested that the same article mentions sauerkraut. I've seen sauerkraut in the fridge at the naturopaths's shop, but she doesn't make it with salty water. She says dogs don't need salt. (I'm not sure I understood that correctly. I'll check next time I'm there.)
Skepvet has looked at studies dealing with the use of probiotic supplements for cats and dogs, and I find that site interesting. But that's supplements, not actual foods like sauerkraut and kefir. The site says, 'There is no high-quality, consistent evidence for most suggested uses of probiotics.'
On the other hand, my doctor recommends the use of probiotics after antibiotic usage (in me, a human), and I suppose at least some of the studies on that topic were conducted on animals.