Police say Kirkly was clocked speeding around 9:49 a.m. on Monday in the area of Commons Blvd. near Reads Way.
An officer tried to pull Kirkly over, but authorities say he sped away to avoid capture.
During the chase, police say Kirkly hit a parked car at the New Castle County Government Center at 87 Reads Way. The car he struck then hit another car.
Kirkly bailed out from his vehicle and ran into a nearby wooded area.
The search for him continued on Monday afternoon.
Anyone with information is asked to call police at (302) 573-2800.