The organic/virgin/unrefined is the best you can buy, and the only king I would purchase for myself or my dog. I've been using coconut oil for years for my skin, and I occasionally put some in my smoothies for an energy/immune system boost! Love the stuff!
I give my 45 lb puppy about 1 tsp per day, sometimes a little more or less. I've heard you can give 1tsp per 10 lbs, but that seems a little excessive to me. I would feed up to 1 tablespoon for a large dog.
I'd say you could work up to 1 tsp pretty quickly or right away for a large dog without any side effects. Especially if you gave half in one meal and half in the other.
If you wanted to increase from that, I would maybe increase by 1/4 tsp every other day. I honestly don't think detox side effects are very common but as with any diet change their digestive system can take time getting used to it. If you give too much, their stool can become greasy... that the only side effect i've seen in my dog when experimenting with dosage when he was a lot smaller.