BuddyPress.org

To be clear, you should see a ‘Take Photo’ link next to ‘Upload’ in the Change Profile Photo interface. See https://postimg.org/image/8q5qy769z/

A first check: Look at the source of the page and search for the string camera_warnings (which should be a list of error messages). If you don’t see this, then it’s likely that another plugin is disabling the webcam feature on the server, using the bp_avatar_use_webcam hook.