I know that a Jiko is a specific contraption for cooking (usually outdoors) in East Africa, but would it be wrong to say "my oven"?
Apparently, even "kitchen" is accepted as translation of "jiko", so I am sure "oven" is close enough.
Actually, "langu" ["my" for sg. of Ji/Ma nouns] and "lako" ["your" (sg.) for sg. of Ji/Ma nouns] have been introduced very early with the noun "jina", but without further explanations. "jina" (name) and "jiko" (kitchen, stove) both belong to the Ji/Ma noun class; possessive starts with "l" (for singular). I hope this helps you in the meantime: I expect that there are tips and notes for the upcoming skill "Ji/Ma" and that these will provide you a complete explanation. [https://www.duolingo.com/skill/sw/Ji_Ma-Nouns/tips-and-notes]. And no, this is not the end of saying "my", because there are more noun classes, and additionally you have to distinguish singular from plural for each noun class. [edit 28-May-2018]
Mambo rafiki! =)
There are many words in Swahili to translate my (actually it is only one, -angu, with all the different concording prefixes), and there is an order (I mean a very good order of structures) to learn all the forms corresponding to each noun class and the concords. Perhaps, it would be a good method to learn first all the forms of possessives, and corresponding prefixes for adjectives and verbs for the the 1st and 2nd class (M-WA), and then for other classes for objects, animals, etc. But in other classes there are also nouns for people, so it is important to know if the concords in the verbs and adjectives are for people, animals or things, groups of animates or inanimates.
Once we learn to understand and make sentences with the noun class for people, then we can start with sentences that describe animals, objects, and ideas with all the concords for adjectives and verbs corresponding with those nouns.
Here is a sentence with jiko and with other objects. In this example, jiko la umeme would be an electric stove.
Kwa mfano, jiko la umeme ni chombo kinachopasha moto, kompyuta inaweza kutayarisha habari na kupiga hesabu, nayo televisheni inaweza kuonyesha picha na kutoa sauti.
Translation (from Glosbe)
For example, a stove can be made to generate heat, a computer to process information and perform calculations, and a television set to produce images and sound.
This is the kind of sentences that I would like to understand when I read a web page in Swahili. But the first group of sentences in Duolingo describes mainly the actions of people. Then, all the nouns and personal pronouns need the verbs and adjectives using the corresponding prefixes. When the subject is not a person, or the object described is different from people, all the verbs and adjectives for these nouns need other structure of concords, that can have other prefixes as ki- / vi-, i- / zi-, li- / ya-, etc. for the verbs and also their corresponding prefixes for the adjectives.
To see a table of concords, here is a list of translations (concords) for MY (-angu):