Williams secured an early break in Flipkens's first service game before holding her own to take an early 2-0 lead.
She then broke and held again to stroll into a 4-0 advantage.
Flipkens, the 12th seed, offered little resistance but did manage to stop the flow of Williams and register her first game of the match at 4-1 after saving a break point.
However, she was struggling to deal with Williams's play and slapped down a double fault to hand the American the first set 6-1 in just 28 minutes.
The match continued in the same manner at the start of the second, although Flipkens did push Williams hard and almost broke her opponent but sliced a backhand wide.
After going further behind, Flipkens finally made inroads on the Williams serve, breaking to make it 2-1 after a slow second serve from the American.
Williams broke at 4-2 to regain the advantage after Flipkens hit a forehand into the net.
The contest was over soon after as Williams racked up three match points. The first went begging but a long forehand from Flipkens gave her the win, 6-1 6-2.