작업걸다 is common word in this case, I think. we use this many case actually. it can be used among strange or someone you already know. and I'm not so sure it's exactly same as flirting though, we use this when you keep talking, texting and asking to go out to someone with certain purpose. eg. 그 남자애가 좋으면, 네가 먼저 작업 걸어봐~