How can I set up an email alert on my iPhone 6 or iPad
Apple allows this with the VIP functionality


Set up notifications for the mail app (inside the settings app) to have whatever push alert you want for VIP email. You can get sounds, etc...
Then add the mail senders you want to VIP status. 


Apple documents this second step here: https://support.apple.com/kb/PH12515

You will want to be sure your email is set up to push email to the phone. Otherwise,  forward those emails to your iCloud address if that’s the only way to get VIP alerts.