How to get started?
I'm a danish teacher. I teach english. When I try to sign in, I can't choose I teach english??
Unfortunately English for Danish speakers is not yet active on duolingo -- I am not even sure if it is in the "incubator" (i.e., if they're currently working on it). What you can do, depending on the level of your students, is work on the "reverse tree", selecting Danish for English speakers. If you have students who are advanced enough to follow the webpage in English, then they can do the exercises and get practice this way. (You can turn of the speakers and the microphone so you don't have to practice saying/listening to things in danish!)
I am not even sure if it is in the "incubator"
It's not. You can check it either on the incubator's page or on these two Duo Wikia pages here and here.
And last news about it was that Duo doesn't place the creation of this coure as a priority to create this course (same for EN<-SV, EN<-NO, etc.) because most of Danish people already learn very good English at school.