Box for Teams Integration for Private Channels
Today, Box for Teams Integration does not support Private Channels.
https://support.box.com/hc/en-us/articles/360044673394-Box-for-Teams-FAQ
Many customers are using Private Channels and need full integration between Box and Microsoft Teams. We do want Microsoft and Box to work together to improve it.

This limitation is due to Microsoft’s platform not allowing integrations to surface as messaging extensions (Box icon to upload and share documents). Until Microsoft supports this for third parties, Box is unable to deliver this functionality. We are working with Microsoft but there is no timeline for delivery at this point.
-
Michael Steinhofer commented
How has this not been resolved? For me it's a security/compliance issue that all of our teams and channels are private so that users who shouldn't have access can't just poke around and see whatever they want. Seems odd to me that Microsoft can't change this?
-
Vincent commented
Hi, our organization has mutliple Teams tenants. We would like the ability to allows all our users to access the Box app in Share channels that are accessible to users on any of our tenants. We understand this could be done by enabling the app on O365 as part of B2B connect, but the Box app is not supported in shared channels presently.