"There is fire in the kitchen."
Translation:Il y a le feu dans la cuisine.
That's an expression that you have to learn as is. A similar expression, "il n'y a pas le feu", means "calm down, there's no rush".
How would you say, in English "il y a du feu dans la cuisine", meaning there is a fireplace there?
It would depend. I don't know of anyone who has a fireplace in the kitchen, with the exception of a couple of people who have wood-burning stoves in their cabins (for heating and cooking). In that case, I would just say, "There's a woodstove in the kitchen."
Wouldn't we use "un foyer" in French, rather than "feu" to mean a fire as in a fireplace?
"Un foyer" is not very much in use in that sense (mostly to mean "household").
I have a fireplace in my kitchen at the countryside...
If they want the literal translation, they should use "Il y a du feu dans la cuisine." This sentence just is weird in English.
"il y a du feu dans la cuisine" would mean there is a fireplace.
"il y a le feu dans la cuisine": please call the firemen!