When someone tells you to go fly a kite it means that you're being annoying to the person or bothering them to the point where they want you to leave and leave them alone.
So basically go fly a kite is just a saying and idiom meaning to get away from them just like someone would say take a hike.
The person saying go fly a kite or take a hike is telling you to get away from them and leave them alone.
It doesn't always mean they hate you but it just means they want you to leave for awhile so they can be alone without you.