Hey Brian,
This is more about xFlow interface's native notifications as opposed the CA Service Management mobile app's push notifications.
Drew,
Push Notifications in the app is still something that's an Idea - Pop Up/Push Mobile App Notifications which is under Review.
One option with in SDM's native functionality is - create a notification method against email addresses of the format 1234567890@phone-carrier.com (in the US, each phone carrier allows TXT messages be sent to an email address of similar format). Utilize this notification method against some activity associations that you want analysts to get a text on.
This way you can actually send notifications as SMS to the analysts? Maybe that's something you can consider?
_R