Yes, DVD players may be used on any flights.
A few reminders... First off, it would be a good idea, if you don't have one, to get a case for the player. When you are boarding the SWA flight and getting seated you have to either place the carry-on in the overhead bin or under the seat in front of you. You won't be allowed to hold it, per FAA regulations. If it is in its case, it will be easier to place under your seat for easy access once the jet reaches 10K feet and you may use electronic equipment. Also, be sure that, if sitting with others, to get there to the airport as early as you can or get your boarding pass online since you want to make sure you get an "A" boarding pass. Also, sound cancelling headphones would be a good investment since a jet cabin can get rather noisy. Also, remember, they prepare for landing with about 10-15 to go in the flight. At that time, they will make you turn off all eletronic devices and stow them for landing.