As noted, this has been an issue for some carriers for the last few years, as different segments of the same airline's flight number are assigned to different aircraft; and, due to delays, two aircraft using the same flight number, may be in the same en route center's (or tower's or TRACON's) airspace at the same time.
For example, United 262 may be a SFO->DEN flight; and United 262 may also be operated by a different airplane, DEN->PHL. If the first segment is late into DEN and the airline doesn't hold the second segment, there'll be a number conflict. The solution for some carriers at least in domestic airspace, is to add a letter after the flight number, so for example, 262Q and 262T, keeps them apart in the ATC computers.