Seeking her first LPGA Tour win in more than two years, Davies sliced three strokes off Kung's lead with one round to go.
Kung let the field make up ground. The 22-year-old from Taiwan, who lives in California, carded a 1-under 71 for a 54-hole total of 14-under 202.
Kung is trying to join Swedish superstar Annika Sorenstam and Australia's Rachel Teske as the only LPGA players to win consecutive tournaments this season.
Davies thinks it will take at least another 66 to win.
Korea's Hee-Won Han is two strokes off the lead and Karen Stupples is four shots back at 10-under 206. Former champion Rosie Jones is among four tied at 9-under.