In clasical arabic (even in standard one) the affixed pronouns are ي ،كَ ،كِ ،هُ ،ها for the singular. To say « your husband », I used to write :زَوْجُكِ (in french « ton mari ») and to say « your wife » زَوْجَتُك (in french « ta femme »). So, the form of duolingo seems to be a dialect. Is it valable for all the arabics countries ?
Duolingo uses some dialectical Arabic for a number of things, and I'm still trying to correct some ideas for people who ask about them in the Sentences section.
As you have noted, the possessive pronouns in Arabic come at the end of the word, and for 2nd person male, it is (-ka) and for the 2nd person female it would be (-ki). There is a tendency however in Standard Arabic as well, when the word comes at the end of the sentence, we would drop the vowel as it is not needed to continue the speech since the sentence is over (or we come at a pause in the speech). So, the (-ka) and (-ki) would end up as (-k), as simple as that. Take things further, maybe one can just add the vowel to explain that a female is spoken to, so (-ki) is used instead of silent (-k); Same thing in writing.
Now, for dialects; Each to its own system. The Levant and Egyptian ones have a tendency to shift the (a) and (i) before (k), thus becoming (-ak) instead of (-ka) and (-ik) instead of (-ki) in standard Arabic. This is of course accompanied by a change in the vowels of the rest of words as well of course. For example (your wife) in standard is زَوْجَتُكَ (zawjatuka), while in the Levant and Egypt it would be zowjtak, zoojtak, or even completely different word in Egypt: mirátak.
On Duolingo, things are mashed up. Once I see a Levant influence, then an Egyptian one, and the audio or speech machine is completely automated giving wrong spelling and even funny pronunciation for some words, and needless to say, wrong grammar.