At least for some form of mechanical clocks: There is an app for that :)
E.g., for Android, the "Watch Accuracy Meter", which can be found in the Play Store or the APK source of your choice, uses the phone's microphone to measure the frequency of mechanical watches.
The Atmos does not have a seconds hand. All models except two do not have minute indications.
I believe that is going to difficult measuring accuracy. You can approximate something if you compare it over a long period of time, perhaps at 12 o'clock, or as much 12 o'clock as you can tell by inspecting the hands alignment.
E.g., for Android, the "Watch Accuracy Meter", which can be found in the Play Store or the APK source of your choice, uses the phone's microphone to measure the frequency of mechanical watches.