옷깃 usually means the edge (especially frontal or bottom edge) of your jacket, and 스치다 to brush (barely touch) by something. So 옷깃을 스치다 means to brush by someone, sort of a metaphor for having an insigniificant encounter with someone. 인연 in its simple sense means an (unplanned) encounter or connection between people. It is also a Buddhist concept of preexisting connections between people (that they are not even aware of) because they were related in their previous lives, i.e. in an earlier cycle of reincarnation. There is a proverb connecting these, which is 옷깃만 스쳐도 인연이다 (or 오다가다 옷깃만 스쳐도 전생의 인연이다 in longer form), meaning "Merely brushing by someone means you're fatefully connected to that person". It teaches that even such a small coming together can mean something profound, and therefore people should never make light of anyone they meet in their lives, as each relationship is a precious one. Your sentence "우리 옷깃을 스치면 인연이 될까?" roughly means "If we brush by each other will that create some (special) connection between us?". 옷깃을 스치면 in this case probably means meeting face to face for the first time. It sounds as if the speaker wants to have a more meaningful relationship with someone they have known through correspondence only. But of course, it's just a guess.