If someone is flying a kite, they are suggesting ideas or possibilities in order to see how people react to them before making a decision about them. The committee has paid a good deal of attention to what might be politically possible. It is consciously flying a kite. The idea came from a senator, but it seems likely that he was flying a kite for the secretary of state. Note: You can also talk about kite-flying. Bracken says he does not want to start kite-flying for his candidacy.