What Chingon and Construct said was fully consistent with what I said, and Chingon, at least, seems to me to be essentially making part of the same point as me: “natural flavors, by definition, have to be additives and not the main substance itself”. You apparently did not understand it, so I thought it might be helpful to spell it out more completely and in more detail. Apparently you still do not understand and you remain confused, only now you are getting truculent about it. Perhaps you should try reading my post again, carefully, and you might finally get the point.
If as you now appear to be saying, you didn’t mean “natural” when you said “natural” and you did not mean “flavors” or “flavorings” when you said “flavors”, perhaps you should take a deep breath, find a dictionary or something similar, and figure out what you did mean, and what the proper words for it are. As it stands, the only possible answers to your question are either “No, foods cannot be made entirely of flavors, natural or otherwise,” or (on a more unconventional, but not absurd interpretation of “flavor”) “Yes, foods can be made entirely of natural flavors, and many (including your example of a cake) are (indeed, maybe they all are, on a sufficiently liberal interpretation of ‘natural’)”. Take your pick. It all depends on what the hell you think “natural flavor”, or maybe just “flavor”, means, something you still seem very confused about, though you are not prepared to admit it. You need to understand that being a “flavor” or a “flavoring” is not a property a substance has intrinsically, it is a property it only has in virtue of being used to give flavor to something. Vanilla pods are commonly used for flavoring, but if I am using one to prop the door open, it is not being a flavor or flavoring right now.
If you are asking whether substances such as those listed at the link given by Construct (i.e., substances that the FDA permits to used as, and listed as, “natural flavors”) can be eaten (either singly, or mixed with one another, but not mixed with anything not on the list) in more than the tiny quantities in which they are normally used for flavoring other foods (i.e., if you used things normally only used as flavorings as though they were foods in their own right), the answer is probably “Yes, you could eat it, but it would almost certainly taste horrible, provide little if any nutritive value, and would quite likely make you ill.” Whether you count that as “being a food” is, again, up to you and your interpretation of those words.