At this young age, I wouldn't give them to him directly unless your doc tells you specifically what kind and what dosage. I would just take some yourself and let it pass through your breastmilk.
I did start giving my kids Udo's Choice Infants Probiotic of Baby Jarro powder in their formula or drinks when they turned 3 months old. I think 1/8 of a teaspoon. Now they are 2 and 4. I make sure they get their probiotics at least 2-3 times a week, multivitamins and fatty essential oils everyday (my kids love the Yummi Bear vitamins and 3-6-9 bears). Other than a few colds here and there my kids haven't been sick. Neither has had to have any antibiotics for anything. And their BM's are regular....my 4 yo goes twice a day and my 2 yo goes 3 times a day.
The probiotics really help to keep the digestive system healthy and running smoothly. Which then in turn helps the body to better digest and absorp the nutrients we put into it. Which then affects our hormones, brain function, muscles, bones.....you see the whole circular effect going on.
So probiotics are all good...just be sure to give him the right amount or he could get diarrhea from it since it gets the digestive system going.