I've had success twice. The first time was via the Delta app on my iPhone during a flight using Delta's wifi. The Delta app brings up the iPhone messaging app. Even if you are logged into the app you have to log in again (so you need your frequent flyer number and password available.)
The second time, I can't remember whether I launched the messaging app from a computer browser or my iPhone; suspect it was a browser because I was at home and I think I remember using the keyboard.

Based on a reddit thread on July 9 when NE flights were again in chaos due to weather, I suspect that if the app isn't working it's because the real human agents are overwhelmed with requests.

(For the curious about What Else Can Go Wrong, my panicked messaging during the flight was because the "My Flight" display on the seatback screen was showing the wrong flight - it was showing the aircraft's next trip which was the return of the flight I was on. I was flying IAD-SLC. So I was seeing a very late arrival time which would cause a missed connection. However, I was actually seeing the arrival time for the return flight SLC-IAD back to my departure airport. )