I'm interpreting this question as "Are there flights whose scheduled local arrival time is numerically earlier than scheduled local departure time?" All other interpretations appear to be silly(ier).
This will be satisfied by any flight of less than one hour duration which crosses a time zone boundary westbound. I thought of looking at flights into Chicago: it is near the edge of the Central time zone, but many nearby cities are in the Eastern time zone. I looked at a United Airlines timetable to find short flights from Chicago to destinations to the east, then looked up the corresponding westbound return flights.
The shortest such flight I found was United 5848 which departs South Bend, Indiana (SBN) at 4:33 PM EDT and arrives at Chicago O'Hare (ORD) at 4:20 PM CDT, a duration of 47 minutes. It only operates Saturdays. Recent FlightAware data suggests that SBN-ORD flights may have an actual flying time as short as 18 minutes. The airports are only 135 km (84 mi) apart.
There were other sub-hour flights from South Bend, as well as Muskegon, MI (MKG), but not as short as UA5848. Intriguingly, there are flights to Chicago from Fort Wayne, IN (FWA) and Grand Rapids, MI (GRR) scheduled for exactly one hour, so in terms of local time they arrive at the same time as they leave. An example is United 5345 which departs Fort Wayne at 4:25 PM EDT and arrives Chicago at 4:25 PM CDT.
American Airlines also has Chicago as a hub and had sub-hour flights from Fort Wayne and Kalamazoo, MI (AZO).