Hello linuxgurugamer,
I have this same issue at the moment. It started after updating to 1.8, so I downgraded to 1.7.3, which also didn't work so I did a clean install and added no other mods except the dependencies. I installed using CKAN.
The problem remains, I assign the axis and buttons and the controls show as working in the AFBW calibration screen. The buttons work but the axis do not. Save, exit, reload, rinse, repeat the they still don't work. Also, sometimes the button and axis mappings don't save, however the name of the preset profile always does. Also, when the ticks for SAS and throttle override are set the keyboard doesn't control the craft.
Here is a log file I just made reproducing the problem, it is in 1.7.3 with all of my mods installed, this install used to work. If you would like I can do a clean install and try it again too.
Log File: https://drive.google.com/open?id=1l5HQFR0HP2PWa6lPL1zJm85uaQazfM62
Thank You! Your Mods make this game very enjoyable for me and my sons!