Yes its okay to give basil. If its fresh give it very sparingly (like a small pinch once a month) but if its dried you could give him a little bit more than that but I would still do it only once a week, maybe every other week. Watch their poop, they could get the runs (if this happens just dial down how much you give them or space it out more). I would make sure theres not too many chemicals/preservatives though first.
Chins can also have dandelions, parsley, oregano, mint, thyme, and cilantro. Again its probably better to give it to them dry and watch their poop at first. I would use just a very small amount once a week for each to find which my chins like
Hope this helps and sorry it took so long for an answer! I totally thought I responded to something very similar to this, or maybe I'm just loosing my mind!