I booked a flight for my daughter last fall and used my husbands RR points to pay for it. It was very easy.
This is from their FAQ:
Can I book travel with points for other Passengers (not me)?
Yes. The Rapid Rewards Member who owns the account from which the points will be used will need to make the reservation for the person traveling. Simply get the destination, travel dates, and flight times from the person who will be using your points and log in to your account via Southwest.com to book the reward travel. A Passenger traveling on a ticket using points from another Member's account will not be allowed to make changes to the itinerary. The Passenger must contact the Member and have the Member make any necessary changes. All reward travel is subject to taxes, fees, and other government or airport-imposed charges of at least $5.60 per one-way trip, which must be paid with a credit card, travel fund, or Southwest gift card at the time of booking. Applicable taxes, fees, and other government or airport-imposed charges can vary significantly based on your arrival and departure destination.