I found the answer. Seeing is believing. It works!

This workspace grabs a File GDB and zips it up to folder of my choice.

This method works best for zipping entire File GDBs with many Feature Classes; in my case, I have 22 Feature Classes. If you have only a couple of Feature Classes, you could zip the File GDB using a File GDB Reader, which will bring in each Feature Class as a separate Reader into your workspace. You then add separate File GDB Writers for each and choose the Zip option in the Writer. 

Does anyone have a different way to do this? Curious to know. 

Feature Writer Parameters from above screen capture:

Hi ​@vxn43 ,

I think File Copy writer can be used to create a zip archive containing File Geodatabase dataset (*.gdb).

1. Create a feature which has an attribute named "filecopy_source_dataset" storing the target File Geodatabae dataset (*.gdb) path.
2. Connect the feature to a File Copy writer, and set the writer parameters as in:
   • Dataset : Add suffix ".zip" to the destination folder path.
   • Surfolder Name : A preferable subfolder name. You can set "." if you don't need to use subfolder.
   • Copy Source Folder : Set "Yes".

Instead of regular writer, FeatureWriter (Format: File Copy) can also be used, as shown below.