While cruising at FL 350, the flight experienced a flame-out of both engines. The crew declared an emergency to Salt Lake ARTCC and the flight was vectored toward Page, AZ for a possible emergency landing. At 12,200 ft, the captain restarted both engines by switching the center tank boost pumps on. The aircraft then climbed to 17,000 ft and diverted to Las Vegas, landing at 1604 without further incident. The flight had departed Minneapolis with the proper fuel load. However, the crew was distracted from the climb checklist after departure by a heading change and a knob coming off the digital flight guidance system while the captain was setting in a new heading. As a result, the item of 'fuel pumps-checked' was missed and the center tank pumps were never turned on. During the restart, the captain realized the omission and corrected it. The flight had been on the main tanks which were exhausted causing the flame-outs. The center wing tank contained about 13,500 pounds of fuel.