With tung oil, you have to reapply every so many years when it wears thin. Otherwise, parts of your floor become unprotected from water. A very important consideration, especially in the kitchen. Also, with tung oil, you will grind all kinds of dirt into the wood.
A superior finish is to use poly. Hier a professional to put 3 coats of oil-based poly down, and your set for 30 or 40 years.
Also keep in mind the higher the gloss finish, the more dirt that will show. All my parquet oak floors have satin finish poly, and the floors never look dirty. This would be especially true in the kitchen. I have 1400 square feet or parquet oak floor but not in my kitchen. The kitchen gets more traffic than any other area, so I prefer vinyl or something that you can afford to replace after 15 or so years.