You can disable the notifications for Airmail in two ways. 

1. System Preferences

Notifications for Airmail can be disabled from System Preferences which is illustrated in screenshot below:

2. Airmail Preferences

Notifications for Airmail can also be disabled from Airmail itself by clicking Preferences > General > Notifications and the same has been illustrated here under: 

Additionally, Airmail also allows its users to disable notifications for one particular account by steps as Preferences > Accounts > More > Notifications. Please refer to the picture below:

Did this answer your question?