I use a rechargeable external battery to charge my phone. Even a small one would be OK for 9 hours of use, when you have your phone's battery near 100% when boarding.

And I agree with ursine -- the WiFi is unreliable. Be prepared to complain to Southwest if you have problems. They will refund your $8.

I fly weekly and generally try to use the WiFi when it's available (for me it is "free"). In my experience it works OK about 75% of the time. OK means: fast enough to do email and websites with limited graphic content. For the other 25% of flights, it is either broken altogether, will not logon to the server, or logs onto the server but is so unresponsive that it is useless. Service suffers when the aircraft is banking to change course. Service does not seem to be influenced by the number of passengers on board.