On a rain-affected third day, Flipkens won 4-6, 6-4, 7-5 and will play Magdalena Rybarikova for a place in the quarterfinals.
Third seeded Sorana Cirstea of Romania beat Tsvetana Pironkova 6-4, 6-4 and Francesca Schiavone, the 2010 French Open champion, was given a tough workout by Nadiya Kichenok before coming through 7-6 (4), 6-2.
Kristina Mladenovic and Bojana Jovanovski were among the other seeded players to progress but it was a disappointing day for the home contingent, with seventh seeded Laura Robson and No. 14 Heather Watson being two of three Britons to be eliminated.
Results from the third day of the WTA Birmingham Open on Wednesday (x denotes seeding):
Francesca Schiavone (ITA x15) bt Nadiya Kichenok (UKR) 7-6 (7/4), 6-2
Marina Erakovic (NZL) bt Ekaterina Makarova (RUS x2) 7-6 (8/6), 3-6, 6-0
Magdalena Rybarikova (SVK x16) bt Mathilde Johansson (FRA) 7-5, 6-7 (4/7), 6-4
Sabine Lisicki (GER x5) bt Kristna Plskova (CZE) 6-4, 6-2
Sorana Cirstea (ROM x3) bt Tsvetana Pironkova (BUL) 6-4, 6-4
Bojana Jovanovski (SRB x13) bt Andrea Hlavackova (CZE) 4-6, 6-1, 6-4
Maria Sanchez (USA) bt Alison Van Uytvanck (BEL) 7-6 (7/3), 6-3
Alla Kudryavtseva (RUS) bt Heather Watson (GBR x14) 6-4, 6-3
Mirjana Lucic (CRO) bt Yanina Wickmayer (BEL x9) 6-4, 6-0
Daniela Hantuchova (SVK) bt Laura Robson (GBR x7) 6-3, 6-4
Kristina Mladenovic (FRA x12) bt Johanna Konta (GBR) 6-4, 6-1