There is a very annoying glitch that affects my friends and myself on Skype during our Xbox One experience. Whenever anyone calls another person, when you accept the notification, you will be directed to skype and then join the call only if it isn't the "no video" option. But that isn't it. After accepting the notification, or not, it will always prompt you with an infinite amount of call notifications for about five minutes even though there was only one call invitation sent. This makes Skype a lot more difficult to use on the Xbox One and the many notifications always disrupt and take up space when you accept the call.
The only solution to do now is to invite the friend when they are on the Skype application at the precise moment as they not encounter the notification glitch.
I hope you patch this glitch that me and my friends have all been experiencing as this will make calling each other a lot more easier and we can also call each other whenever we want, as the notifications will be fully functional.
Sorry to hear you're having this problem; it's not something that we've heard before.
Can you do a test call and note the date, time and timezone of the test along with the Skype IDs/Microsoft Accounts of the participants including yourself. If you can DM me this information I can begin investigating the cause of your duplicate notifications.
We've made some improvements on both areas. Do you still see those issues in the latest Skype 1.8 for Xbox One?