No. Your Xbox friends cannot see video from your Kinect.
Why It's Impossible
Architecture: Kinect (v1 Xbox 360, v2 Xbox One) streams depth/IR/color data to the local console only for skeletal tracking, voice recognition, and sign-in. There is no API, service, or UI to broadcast this feed to Xbox Live friends.
Privacy by Design: Microsoft explicitly never implemented "Kinect sharing" due to privacy, bandwidth, and liability concerns. The "Kinect Share" feature in Kinect Fun Labs let you upload still snapshots you explicitly took—not live video.
Hardware Limitations: Upload bandwidth (especially on 360) couldn't sustain 30 fps video + game traffic. Xbox One reserved USB 3.0 bandwidth for Kinect v2 local processing only.
Software Removal: Xbox One launch allowed "Kinect as webcam" for Skype/Upload Studio (opt-in). This was removed in 2017 dashboard updates. Series X|S do not support Kinect at all (no port, no driver).
What Friends Can See
Your Gamertag, avatar, profile bio, real name (if shared).
Online status: Online / In-Game / Party / Looking for Group.