Speaking as a total ignorant from a coding perspective. But I guess that wouldn't be the hard part, considering that most of Duolinguo is just boxes and text inputs. How difficult it is to create a database of competent linguists with an efficient training who can progressively enhance your understanding of languages?
Let's not overstate Duolingo's effectiveness for language learning.
The technological challenge to adopting a self-taught language learning method into an app is rather small. You just need the content. Either you develop the course under a Free Culture license, or you purchase the rights for an existing method and you port it. Plus maybe some volunteers to handle user-interaction.
A good example is the VHS Lernportal which implements three levels of German class in a way that actually has some pedagogical merit. It's killer-feature is nothing technological, but that they have some teachers in the backoffice that will read your occasional text-production exercises and offer corrections (no, language tool wouldn't be able to replace humans in that case, because language tool doesn't know what you are trying to say and therefore gives you multiple guesses but no way to know which one you actually need).