I've been getting flight updates as text for many years from United and Delta. If they can do the e-mail, there's probably a pull down on the settings page to also send them as text to your phone.

I love it, land for a connection, turn the phone on, and the message comes in telling me what gate we are pulling into and a few seconds later another one saying where the next flight is leaving from, and if we were delayed they may have already rebooked me on another flight for the missed connection.