To do something on the fly is to do it quickly. When people rush, they’re working on the fly.
Sometimes people take their time, doing things slowly, carefully, and deliberately. Other times, they do things on the fly. When you do something on the fly, you’re doing it fast and probably not carefully. A student scrambling to finish some homework on the school bus is working on the fly. A teacher who instructs the class without planning a lesson is teaching on the fly. This phrase applies when you have to work fast and without preparation.
on the run or in a hurry“she wrote those letters
on the fly”