"kitchen" is "kuchnia". Theoretically "kuchenka" could be considered "little kitchen", but that's an overintepretation.
Kucharz and kucharka are "cook", not "cooker". A cooker is a synonym of a stove. And as Wiktionary (see here: https://en.wiktionary.org/wiki/cooker) does notice that it is chiefly British, I guess "stove" should be the default English answer, as Duolingo focuses on American English.