"In" can be used for both Akkusativ and Dativ. The rule for distinguishing between them is to ask yourself if there is a movement to a place or whether it describes being at a place. In this sentence it is a movement into the kitchen, which makes it Akkusativ. It would have been Dativ if "in" was used for describing being in the kitchen.
This is a whole group of prepositions. to make it easier I divided it into two groups: "auf" and "über". If it is non-dynamic (stays within an imaginary box) you use Dativ, otherwise always Akkusativ. With "in", "an", "hinter", "neben" "unter", "vor" and "zwischen" you ask if it changes from one box to another (from your hand into the cupboard). In that case you use Akkusativ, otherwise Dativ. Works like a charm.
Into implies you're entering a place. In implies you're already there. For example, "You walk into the kitchen." would mean you entered the kitchen. "You walk in the kitchen." means you walk around the kitchen, implying you're already there and walking within the confines of the kitchen. Since this sentence is using accusative, it implies that "in" translates to "into" and not "in".
Another example could be, "You walk into the wall." vs. "You walk in the wall." They would mean very different things!
As an addition to what darkadegeron posted, this verb requires especially delicate consideration since it is commonly used as an explicit colloquialism. Which meaning is conveyed depends on the whole prepositional phrase: "...into [most place nouns]" is unambiguously innocent, but "...into [most non-place nouns]" is unambiguously not (if even intelligible). Be wary of this verb.
In my dialect of American English, the sentence you posted reads explicitly, but could be reasonably assumed to have been intended as either "coming into the kitchen" or "coming in through the kitchen".
I don't understand why "You are coming in the kitchen" isn't correct. I'm a native English speaker and use in and into interchangeably when showing direction.
For example: The train went in the tunnel. I went in the store to buy chocolate. When I came in the house I got mud on the floor.