Mac Mail on El Captan malfunctioning One draft window flashes continually on and off the screen even though I have deleted the draft from my menu on the left. 

Any ideas on what's causing this and how could I fix it?
I have a workaround in mind that would benefit you more then it would hurt you. You can always use a secondary mail client like CloudMagic, which I used for a while. I haven't used the default mailing client for at least 2 years now. CloudMagic is free on the Mac App Store and for iOS.