21 CFR 101.22
(a)(1) The term artificial flavor or artificial flavoring means any substance, the function of which is to impart flavor, which is not derived from a spice, fruit or fruit juice, vegetable or vegetable juice, edible yeast, herb, bark, bud, root, leaf or similar plant material, meat, fish, poultry, eggs, dairy products, or fermentation products thereof.
(3) The term natural flavor or natural flavoring means the essential oil, oleoresin, essence or extractive, protein hydrolysate, distillate, or any product of roasting, heating or enzymolysis, which contains the flavoring constituents derived from a spice, fruit or fruit juice, vegetable or vegetable juice, edible yeast, herb, bark, bud, root, leaf or similar plant material, meat, seafood, poultry, eggs, dairy products, or fermentation products thereof, whose significant function in food is flavoring rather than nutritional.
So this is "natural flavor"
(i) If the food is one that is commonly expected to contain a characterizing food ingredient, e.g., strawberries in "strawberry shortcake", and the food contains natural flavor derived from such ingredient and an amount of characterizing ingredient insufficient to independently characterize the food, or the food contains no such ingredient, the name of the characterizing flavor may be immediately preceded by the word "natural" and shall be immediately followed by the word "flavored" in letters not less than one-half the height of the letters in the name of the characterizing flavor, e.g., "natural strawberry flavored shortcake," or "strawberry flavored shortcake".
(ii) If none of the natural flavor used in the food is derived from the product whose flavor is simulated, the food in which the flavor is used shall be labeled either with the flavor of the product from which the flavor is derived or as "artificially flavored."
(iii) If the food contains both a characterizing flavor from the product whose flavor is simulated and other natural flavor which simulates, resembles or reinforces the characterizing flavor, the food shall be labeled in accordance with the introductory text and paragraph (i)(1)(i) of this section and the name of the food shall be immediately followed by the words "with other natural flavor" in letters not less than one-half the height of the letters used in the name of the characterizing flavor.
So the "natural" portion of your labeling is in regards to the source of the flavor ingredients. In this case they're of plant origin so "natural" for the purposes of the ingredient statement.
If your sauce does not contain truffles as an ingredient, then it would be labeled "artificially flavored truffle sauce", but your ingredient statement would still list natural flavor as the actual ingredient.
If your sauce does contain truffles as an ingredient, then it could be labeled "Natural truffle flavored sauce" or "truffle flavored sauce" and in the ingredient you would just have "natural flavor"
If your truffle flavor includes both truffle-derived flavors and the bark natural flavors, then it would be labeled "Truffle flavored sauce with other natural flavors".
FDA tends to be okay with using labeling with separation of the words as long as they're both easy to read and on the principal display panel. E.g.
TRUFFLE FLAVORED SAUCE
with other natural flavors
Key point to stay out of trouble as always is to make sure that you don't gain a market advantage over another provider who was using the whole thing using your "artificial" ingredient. That's when FDA/class action's gain traction on labeling.