fly a kite

To fly a kite is to send a lightweight frame covered with paper or fabric into the air, where wind keeps it aloft while you control it from the ground with a string: We flew kites at the beach all afternoon.

Figuratively, to fly a kite can mean to test public reaction to an idea before committing to it—floating a trial balloon.

In British slang, go fly a kite is a dismissive way of telling someone to leave you alone.