I don't know, sounds like some sort of flute - Native American flute, or something? Though, it sounds a bit more electronic?
I guess it could be just a generic synthesized sound, since I've mostly heard it in vidya gaems and all. Doesn't sound too flutish (flutey? flautulent?) to me though, sounds an awful lot like somebody rubbing a wet finger across a mirror or something.
Another example at 0:08 for clarity while I do some XhardXcoreX googling
Nah, I liked it fine, it just never struck me as the GOAT-TV-meisterartwork that it gets hyped as by pretty much everyone... just thought it was a pleasant, standard HBO show. I genuinely wondered if it gets better after the first season á la Sopranos and Oz.