I have uploaded the sample project for you.
Try firstaddon-ArcgisPro project.
It is using the nlog and you can configure where to log in nlog.config
If you have difficulty downloading from github, you can download from this attachment as well.
Let me know how's you go.
I use serilog and log to the folder where the add-in is installed.
I also created a feedback button in my pro addin ribbon that grabs the most current file and attaches it with their feedback message.
The project I am working on is on github, GitHub - agrc/uic-addin: An ArcGIS Pro add-in to help manage, create, and validate the UIC GIS datab...