The 27-year-old Belgian, a semi-finalist at Wimbledon earlier this summer, had her serve broken twice in each set and managed only six points on the Hercog serve, went down 6-3 6-1 in just 54 minutes.
"I actually felt quite okay on the court today - it's just Polona was playing the match of her life, and all I can say is congratulations," Flipkens said on www.wtatennis.com.
"I've had a great year and I'm really enjoying what I love to do, which is playing tennis, and I've really taken a step forward."
Slovenian Hercog will face Julie Coin in round two after the French qualifier saw off Portugal's Michelle Larcher De Brito 7-6 (7/5) 7-5 on Tuesday.
Second seed Kristina Mladenovic of France needed three sets to get past Melanie Oudin, eventually defeating the American qualifier 7-6 (7/5) 5-7 6-2.
Third seed Lucie Safarova and fourth seed Bethanie Mattek-Sands made smooth progress to the second round, Czech Safarova overcoming Georgia's Anna Tatishvili 6-3 6-2 and American Mattek-Sands toppling Canada's Stephanie Dubois 6-3 6-4.
Seventh-seeded American Lauren Davis battled from a set down to oust Italy's Camila Giorgi 6-7 (5/7) 6-3 6-2, while Czech Barbora Zahlavova Strycova - the 2011 champion - advanced with a 6-3 7-5 victory over Greece's Eleni Daniilidou.
There were also first-round wins on Tuesday for Kazakhstan's Sesil Karatantcheva and Croatia's Mirjana Lucic-Baroni.