Sounds like he is a fairly healthy little guy and off to a good strat. Has he had his colestrom from his mother? The reason I say that is from experiences with raising baby calves off of goats milk, its critical they have their colestrom. I wouldn't push him with too much milk right now because his tummy is sensitive and he may scour on you. What we found that worked for us was to give them immediately after we got them, and usually at a day old, was a 7 way tab for scours, etc, can't recall the name of it exactly, but Jeffers sells it, and then we gave Immuno-g, an immune system booster to them and were able to successfully raise them without scour (e-coli) or pnemonia problems. We found that goats' milk didn't cause any constipation problems at all. It was the right millk to feed them compared to milk replacer.
The ones we had problems with had no colestrom and pretty much that was a disaster.
We waited about a week before raising their milk intake and then gradually increased it to a gal a day by the end of their second week. With the method we used we found they were able to tolerate the milk increase easily with no problems.
That was what worked for us, now someone else may suggest something different. They grow very well on goats milk I think. We also found milk replacer does not work as well for calves and goats. Hope this helps.
Bernice