I'm trying to create a way users can select features from our WFS that's running on ArcGIS Server and have it convert them in KMZ or shapefile. We will be using WebApp builder. I'm pretty comfortable with creating a widget or publishing a geoprocessing tool. I'm good with Python and JavaScript.  I'm just wondering what is the best approach. I looked into FME Server, but that costs a lot of money. I'm wondering if there is a way to do it with GDAL - org2org. 
The way we do it now, is the user has to select the features with the select tool in Web AppBuilder. Export it as a GeoJSON and then ship it off to a 3rd party called https://geoconverter.hsr.ch/ . We really do not want to be sending our data there. 

Any ideas on how I can do this? 

I also tried the clip and ship method Esri has recommend but still it will not convert to KMZ unless you have the iterability extension.  https://enterprise.arcgis.com/en/server/10.3/publish-services/linux/gp-service-example-clip-and-ship.htm