Hello Jonni,
Regarding the Echo show side, they need to do the following.
From your Echo Show device, ask Alexa to call one of your contacts.
The person who you are calling will see an image/card of you with the option to accept or reject the call by tapping on their Echo Show home screen buttons or by saying “Alexa answer” or “Alexa ignore.”
When the call starts, say “video on” or press the video camera icon on the screen.
If at any point you want to turn off the video only, you can say “video off” or press the video camera icon again.
When you are ready to hang up, say, “Alexa, hang up.”
On your PC side, be sure the user you are trying to communicate with is added to your contact list.
Open Skype.
Click on Settings.
Under the Voice and Video calls settings, tick the box that says Answer calls automatically.
Let us know if that resolves the issue.