Copy and pasted from the SW site. So, make sure the gift cards are high denominations or plan to buy each ticket separately.
Up to four southwestgiftcards can be applied toward one reservation. Our payment system limits the total form of payments, so, if the balance of the itinerary is more than the amount of all four gift cards, you will only be able to use three of your gift cards so that the balance can be paid with another form of payment that will cover the balance of the reservation (i.e. credit card). The following is our policy in regards to forms of payment: Southwest Airlines accepts up to two unused Ticketless Travel tickets per passenger (are always applied first) and up to four of the following in any combination: southwestgiftcards, Southwest LUV Vouchers, Ticketless Travel Funds (left over funds not previously used), and one credit card.