BlueMail functions independently from all other email applications. You get Instant Notifications, automatic email sync, and have the ability to read your email without being reliant on any other app!
In fact, since BlueMail functions on its own, there is no need to keep any other email client on your device. This way you will receive an email notification just once using BlueMail's Instant Push!
Enjoy our stand-alone app!
If you would like to disable your stock email client or any other email client, depending on the device, you can either go into that application and remove your email account, or you can try to Uninstall, Disable, or Clear Cache from that application in order to not receive any future duplicate notifications.
See here regarding uninstalling preinstalled Android apps.