Narrative:

After landing on runway 36L we exited E2 and was given instruction to taxi via [taxiway] east and hold short [taxiway] J. Approaching [taxiway] J we were given taxi instruction to cross runway 36R at [intersection] wj and contact ground on the other side. I turned the aircraft onto [intersection] wj turned on all aircraft lights and stated that the runway was clear to the left. As we approached runway 36R I heard [another] flight state that they were already past the hold short line. My check airman in the right seat looked right to make sure the runway was clear and applied the brakes as he saw the aircraft on the takeoff roll and lifting off the runway. Stopped in position (just short of the runway or pretty close) and we tried to contact tower several times to verify that the runway was clear and that we could proceed. Tower stated that we were clear to continue and cross runway 36R at [intersection] wj and contact ground. After crossing the runway the check airman asked for a phone for tower to discuss the issue. We contacted our chief pilot's office and safety department.as I wasn't in the tower it would be speculation to what I think the cause was other than situational awareness.

Google
 

Original NASA ASRS Text

Title: EMB-175 flight crew reported a near collision while taxiing at DFW.

Narrative: After landing on Runway 36L we exited E2 and was given instruction to taxi via [Taxiway] E and hold short [Taxiway] J. Approaching [Taxiway] J we were given taxi instruction to cross Runway 36R at [Intersection] WJ and contact Ground on the other side. I turned the aircraft onto [Intersection] WJ turned on all aircraft lights and stated that the runway was clear to the left. As we approached Runway 36R I heard [another] flight state that they were already past the hold short line. My check airman in the right seat looked right to make sure the runway was clear and applied the brakes as he saw the aircraft on the takeoff roll and lifting off the runway. Stopped in position (just short of the runway or pretty close) and we tried to contact Tower several times to verify that the runway was clear and that we could proceed. Tower stated that we were clear to continue and cross Runway 36R at [Intersection] WJ and contact Ground. After crossing the runway the check airman asked for a phone for Tower to discuss the issue. We contacted our Chief Pilot's office and safety department.As I wasn't in the Tower it would be speculation to what I think the cause was other than situational awareness.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.