Flash Pro (or even Animate CC) does not have the ability to do this (search the entire library). You can simply search for elements present in the current scene that might work for you if you have a very small FLA with one scene (see Iggy for this).
You can still search your library by saving the FLA as XFL using File / Save As ... and then search the text files inside the XFL package's LIBRARY folder for the name movieclip / sprite / bitmap / whatever You want to know about the purpose of use.
You can use any command line or graphical tool to perform this search. If you are using Mac OS X, you can use grep out of the box. And if you use Windows, you can install it using cygwin (or use GrepWin, which is a graphical version of grep). The command line syntax would be something like this:
grep -ir "Library Clip Name" .
(if the current working directory is the "LIBRARY" folder of your XFL)
You need to search for "DOMSymbolInstance". Files containing this line when performing the above grep search use this clip (just find the file name on the left, the same name that you assigned in the library window).
You can execute nested grep, so you do not need to manually search for "DOMSymbolInstance" in the output:
grep -ir "Library Clip Name" . |grep DOMSymbolInstance
This is the best and fastest way to get use of a library item in a large FLA / XFL.
If you just want to see the names of library elements without duplication (in case the element is used several times in one clip), use this:
grep -ir "Library Clip Name" . |grep DOMSymbolInstance |cut -d: -f1 |uniq
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