Assistant Chief Brian Schaeffer told The Spokesman-Review the family members were traveling Saturday because the boy's father is being transferred from Joint Base Lewis-McChord.
The boy had been cleared for the flight but suffered a medical emergency. His heart and breathing stopped. The crew performed CPR but couldn't revive him.
The plane diverted to Spokane International Airport, where medics continued CPR without success. The Spokane County medical examiner's office is conducting an autopsy.
Delta Air Lines Flight 128 had 258 passengers on board. Delta spokesman Michael Thomas says passengers later returned to the plane to complete their trip.