Think of what makes a kitchen a kitchen: cabinets, fridge, stove, oven, dishwasher or kitchen sink. This is simply removed and taken with leaving an empty room with the connection points that you would need for a kitchen, but no actual kitchen.
(source: I live in Germany for 2 years now)
If you take 'Kueche' to mean 'kitchen' then a 'separate kitchen' would normally be translated as 'eine getrennte Kueche' - i.e. not part of another room, as in the increasingly common 'kitchen-dining room'. Have a look at some of the on-line descriptions of property for sale or to rent! BUT I think from the context here, a better translation is 'cuisine' (style of cooking) which then makes much more sense, as each person has 'an individual cuisine'; you could also talk of the person's own 'range of dishes' (which they like to either cook or to eat)
Native speaker here. I think a "custom kitchen" would be "eine spezial-angefertigte Küche". If you were to say something like "Most kitchens have a table, but your individual kitchen may look different." you would translate it as "Die meisten Küchen haben einen Tisch, aber deine individuelle Küche könnte anders aussehen." Note that often you will find something like "die Ideen des Einzelnen" for "individual ideas", while "individuelle Ideen" can mean something like "unique ideas" depending on context.
This is the closest thing to an answer. But there is a systemic problem here throughout the DL German course concerning the use of 'individual'. The problem is not with the German word, but with the English word. Because we native English speakers never use the word 'individual' to mean whatever it means here in German. As has been suggested, the word 'unique' seems more likely, but apparently that misses some nuance of the German word. So let's throw it out there: we don't know what an 'individuelle Kueche' is, or how it is different from an 'einzelne Kueche'. Nor do we understand the difference between 'individuelle Tiere' or 'einzelne Tiere'
To get some sense of the native English speaker (somebody correct me or back me up), I say that someone is an individual (noun) to mean either that they are a free-thinking person, or even that they are different from normal, or even negatively that they put themselves ahead of the group. But I never use individual as an adjective in this way. As an adjective, I might emphasize tedium (I have to input every, individual piece of data, line by line, never ending...) I might use it to emphasize a distinction between categories (each individual species of animal has unique traits). But I honestly can't think of another sense in which I would use the English word individual in a sentence, at least as an adjective.
Ergo, either 1) there is a better English word to capture the meaning of the German word (whatever that may be); or 2) There is no English word that means quite the same thing and we need to be taught what it actually means.
I searched for individuell in context.reverso.net, and I found a translated sentence that uses "individuell" within the context of describing a future hybrid of public transport and self-driving individual vehicles - so perhaps a good way to conceive of "individuell" is as the equivalent of the English "single serving portion" or "non-shared."? Wenn Sie sich Ihrem Zuhause nähern, koppelt sich Ihr Abteil ab und fährt Sie direkt vor die Haustür. (And when you get close, the section you're sitting in detaches and self-drives you right to your doorstep.) Es ist gleichzeitig gemeinschaftlich und individuell. (It is collective and individual at the same time.)
I've searched http://context.reverso.net/translation for both "distinct cuisine" and "individuelle Küche" and could not come up with anything, except "separate kitchen" . . . So I think perhaps the sentence "Jede Kultur hat ihre eigene individuelle Küche." is not the same as "Each culture has its own distinct cuisine." after all! :-< Anyone more experienced in German want to take a crack at how to better express that sentence in German?
Google translate again. This is not said in English. I wish DL would remove silly phrases like this. It could make more sense in a complete sentence but I doubt it. There seems to be no consensus in this forum as to what this means even though we all know what the actual words mean. The tips are useless. Good grief!