I always do to women. They only sometimes respond. (I live in a neighborhood of Brooklyn expats.)
Men it depends. If they’re walking with women then of course. If not, it depends which neighborhood I’m in. In my neighborhood, which is very yeshivish, I won’t unless they say it first, and generally they only say it first if they know me (friends of my dad’s, etc). It doesn’t necessarily come up, of course- I’ve often walked down the block and seen a guy cross the street when he saw me approach. Not sure whether to be offended or flattered… 🙂
I don’t think that saying good Shabbos is INHERENTLY flirting. I will definitely concede that in many cases it can be (walking a few shabbosim back with a couple of friends who were prettier than I am, we got a good Shabbos from them that was definitely not just politeness and concern for our well-being…), but it can also just be politeness, which seems to have gone the way of the dinosaur.