Flash Pro (or even Animate CC) doesn't have an option for this (searching your whole Library). You can just search for elements present in the current Stage, which maybe works for you if you have a very small FLA with a single scene (see Iggy's answer for that).
You can still search in your entire Library, though, by saving your FLA as XFL using "File/Save as..." and then searching in the plain text files inside the LIBRARY folder of the XFL package for the name of the Library movieclip/sprite/bitmap/whatever you want to know the uses of.
To perform this search you can use any command line or graphical tool. If you are using Mac OS X you can use "grep" out of the box. And if you're using Windows you can install it with cygwin (or use GrepWin, which is a graphical version of grep). The command line syntax would be something like:
grep -ir "Library Clip Name" .
(assuming the current working directory is the "LIBRARY" folder of your XFL)
You have to look for "DOMSymbolInstance". The files containing that string when performing the aforementioned grep search are using that clip (just look for the name of the file at the left, which is the same name you assigned in the Library window).
You can perform a nested grep so you don't have to manually look for "DOMSymbolInstance" in the output:
grep -ir "Library Clip Name" . |grep DOMSymbolInstance
This is the best and fastest way of getting the usages of a Library item in a big FLA/XFL.
If you just want to see the library item names without duplications (in case an item is used several times in the same clip), use this:
grep -ir "Library Clip Name" . |grep DOMSymbolInstance |cut -d: -f1 |uniq