It means:

Catch up with this spring early, and catkins are already flying all over the sky during the Cold Food Festival.

Explanation of words:

No fire: no fireworks, another name for the Cold Food Festival. One or two days before Tomb-Sweeping Day is the Cold Food Festival, and cooking is not allowed on this day.

Every spring is early: it refers to the actual weather, which heats up early and cannot be interpreted as the festival is ahead of schedule.

Flying flower: another name for catkin.

Town Day: All day.

Busy: personification means flying around people.

Under normal circumstances, after the catkins fly in Tomb-Sweeping Day, it will be earlier because of the warm weather.