The thing about trying to work out food ingredients via analytical chemistry is that it largely boils down to "lots of compounds in ppm, ppb, and ppt quantities" which if you're missing one of them causes the taste to go off. So it will tell you lots of things, but it won't really do anything to clarify what "natural flavors" are in the ingredient list.
IMO, the most distinct flavors in Dr. Pepper are cherry and almond. Benzaldehyde, an "artificial cherry" molecule listed in this spectrometer video, is found in both cherry and almond extracts.
If you're familiar with the taste of amaretto or marzipan, try thinking of those next time you drink a Dr. Pepper. That will unlock the flavor discrimination for you.
You can potentially take a list of the finite natural flavors that are commercially sold in quantities to produce Dr pepper world wide and perform some sort of likelihood analysis based on these concentrations in the sample.
When I was a kid, I had to take this medicine that came in a very cherry-flavored syrup. I hated it. To make it tolerable for me, my parents mixed it into a shot glass of Pepsi.
When I grew up, I tried Dr. Pepper, and immediately recognized the taste.
https://www.youtube.com/watch?v=rcOM3H06KI4