I wondered, it must be possible to analyze the liquids, and from a kind of spectrum and its peak find recognize the signature and the main flavors that are present in the mix ? Do people who are more specialized in chemistry do that ?
An analysis will tell you what compounds are in a juice. But all the flavor concentrates we have available to us are made from multiple compounds. And several of the compounds are part of many different flavor concentrates. So you'll get a list of components - but it won't do you any good unless you have access to all of the flavor compounds that the flavor manufacturers have available to them. It will not tell you which concentrates were used to make the juice.
Your thinking of a technique called chromatography, it separates and quantitates the individual chemicals in complex mixtures. However, it would not be realistically possible to do what you're asking. It wouls take a ton of ground work testing many, many individual flavors to build a database of those individual flavor's chromatograms (the graphical result). Then you would have to attempt to deduce the percentage and identity of those flavors in a commercial flavor, and there will be a TON of overlap in what goes into each. And sadly, that doesn't even begin to address the method development challenge that the technician would have to plan, work, and rework to get any meaningful result. Sorry to bear the bad news.
Luckily, flavour houses exist that do this on the molecular level. When you make your own flavouring, you don't have to compare it against a receipe of other off-the-shelf alternatives, when you've got a good starting point based on the GCMS, you just...make that and then adjust by taste.
If you own every flavor ever made, and have access to a mass spectrometer that you are free to use on your own work, it would be possible. Of course, you would need to ignore ethyl alcohol contents (it disappears with the kind of steep most commercial nuices experience) and you'll need to account for chemical interactions between different flavor compounds, and the offgassing of lighter flavor volatiles from the commercial juice, but.... Yeah, for a mere investment of tens of thousands of dollars and many thousands of hours, you could try it.
Your best bet is to get really good at mixing your own juice, and try to recreate the juice you’re wanting. After so many trial and errors you’re bound to get close.