The trio were the only seeds in action at the WTA International grass-court event in 's-Hertogenbosch and all three successfully negotiated their first tests.
Sixth seed Flipkens was too strong for Polona Hercog as she reeled off the final eight matches after eventually gaining a breakthrough late in the first set.
She joins fellow seed Andrea Petkovic in the second round, while Spain's Muguruza is also through after ending the campaign of Dutch wildcard Lesley Kerkhove with a comfortable 6-4 6-2 victory.
Muguruza, who caused a stir by beating Serena Williams at the French Open recently, was forced out of the Aegon Classic last week due to injury but came from 3-1 down in the first set to progress.
She will face Yvonne Meusburger in the second round, while 2005 winner Koukalova was made to work hard by Spanish world number 53 Maria-Teresa Torro-Flor.
Koukalova moved ahead thanks to a first set tie-break before Torro-Flor hit back to level. However, the eighth seed moved four games ahead in the final set and finished off the job.
Germany's world number 55 Annika Beck was given a stern test by Israeli qualifier Julia Glushko before winning through 7-6 (7-5) 7-5 in just over two hours, while compatriot Mona Barthel is also in the second round.
The qualifier avoided an upset against Maria Kirilenko - ranked 28 places beneath her in the rankings - and won 86 per cent of her first service points to book a place in the next round.
Elina Svitolina breezed through her first round clash with Kurumi Nara of Japan - winning 6-2 6-1 in just over an hour.
Nara failed to take advantage of seven break-point opportunities and Svitolina will be expecting a more difficult match when she meets Flipkens in the next round.
Zheng Jie was too strong for Monica Puig, progressing 6-4 7-5, before home favourite Michaella Krajicek edged out Jana Cepelova of Slovakia.
The Dutch qualifier came through a lengthy encounter 6-3 4-6 6-1 while Coco Vandeweghe also won her three-setter against Marina Erakovic 6-4 3-6 7-6 (7-5).