Fellow Belgian Yanina Wickmayer followed up her title in Linz, Austria, last week by beating Alexandra Dulgheru of Romania 6-3, 7-6 (4). She will play France's Alize Cornet in the next round.
U.S. Open winner Kim Clijsters, a doubles partner of Flipkens, will play Patty Schnyder of Switzerland on Thursday for a place in the quarterfinals.
Clijsters, seeded second, has won the tournament in the Grand Duchy five times.
Top-seeded Caroline Wozniacki of Denmark withdrew in the opening round Tuesday with a left leg injury.
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