The prepositions kun and per can both be translated in English with with.
In this case, which one should I use?
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Per implies, to some extent, that it is your main method of learning.
However, you can use kun as well, or ĉe, or en, or je.
The reason is simple: I would guess what you meant even if you said sur, sub, laŭ, apud, because it's a website, not a physical object, so it's all about the mental image, just as with aludi al io, danci sub muziko, beno sur vi, etc. Anyone who claims that you "can't" use a particular preposition which makes sense to you should be able to justify the assertion—be cautious about accepting attempts to impose arbitrary idiomatic expressions on Esperanto, which simultaneously make it harder for no good reason and subtract from its expressiveness.
The other answer claims that kun can only mean that Duolingo is also learning. This is obviously nonsense. Mi lernas kun instruisto does not mean that the teacher is also learning. Kompari tion kun io does not mean that the thing is also comparing. Ŝi hezitis kun la finado does not mean that the ending is also hesitating.