I wonder how this app works: Obviously it must transmit the highscore quickly enough before the phone shatters. I hope it opens and warms up a connection before you throw it. Maybe it can constantly transmit the height and falling time/speed up until the last second of life of the phone
If the app is indeed able to have a fairly accurate height value, it just needs the turning point height in order to calculate speed, duration of fall, and the (more or lees) exact time of impact. So it could transmit the value whenever it detects that the phone has stopped moving upwards.
You're not going to get the turning point from accelerometer data, as the phone is in free fall the whole time. The non-zero acceleration will be on takeoff & landing (or launch & catch, or impact...).