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: