Had similar problems on my X98 air 3G.
You won’t find any useful answers on Skype.
Fixed mine by uninstalling the front and back camera’s in device manager and installing the camera drivers from this site…. this fixed the upside-down skype image but still left me with inverted images on the front camera ( when using the Win 10 camera app ).
After hours of installing/reinstalling the camera drivers and re-booting the tablet with no change I decided to re-download the camera app from windows play store.
The installation for the camera app tells you that its already installed but click the download button again and it instantly displayed the camera image correct way up !!!.
I still have one remaining problem.. that of HDMI mirrored images on the TV being upside down with the Tabley seated in its holder.
Could someone out there place their tablet in Landscape orientation with the forward camera at the right top (buttons on top right edge ), go to settings > Display and tell me what it says about the screen orientation in this position.
Mine says its ‘Landscape ( flipped )’ ie it thinks the tablet is upside down. I believe this is causing the HDMI image to be presented inverted on the TV compared to this orientation of the tablet ?.