UPDATE – September 16: Microsoft has removed the date from the Xbox One store. We will update if the date changes.
*Beta starts October 21, 2016 on Xbox One. Availability and launch date(s) subject to change. See www.callofduty.com/beta for more details. Minimum Beta duration is 3 days.
The beta will start first on PlayStation 4 on October 14. In order to get access to the beta, players must preorder Call of Duty: Infinite Warfare either digitally or at a participating retailer.
An end date for the betas has not been announced yet.
SOURCE: Microsoft Store