K.Y. (kuuki ga yomenai) means that a person can't lit. "read the air," or can't tell what's happening with the people in the room. For example, if the K.Y. person were a comedian and making jokes that no one is laughing at, s/he (the comedian) would have no idea that no one's laughing and might think that the comedy gig is going fine.
In an everyday life example, it might be someone at a party making offensive jokes. But s/he wouldn't know that people were being offended, and so s/he would be K.Y.
The first time I heard this phrase, several years ago, it was at a nomikai (lit. a drinking party). There was a guy telling stories about his trip to China, and he went on for a long time. He thought everyone was fascinated with his tales and details, but when he went to the bathroom, someone said, "Kare kuuki ga yomenai ne. . ." and I asked for a translation.
Anyway, I don't think that K.Y. is ever intended as a compliment, in Japanese. The closest that I could imagine it to being a compliment would be when used by someone who knows that KY is the abbreviation for Kentucky, if that person like Kentucky Fried Chicken (which here is abbreviated as "KEN-tah-kee," not KFC).
Anyway, some video examples. From a drama:
A video I didn't really understand, to tell the truth. . .
And something else that I didn't understand, because the subtitles were in Spanish. But I thought the video was visually interesting.