The celebrity couple announced their separation last week, days after they got engaged.
Flack allegedly called out Brady for having talks with the E4 reality show in a now-deleted Facebook post.
She reportedly wrote: “When you find out your fiancé had been planning a meeting to go on Celebs Go Dating, and has the meeting the day AFTER you break up.”
Brady has since broken his silence, saying he agreed to the meeting because he was left “crazy” and “irrational” from a lack of money.
In a Twitter statement he said: “I never comment on media speculation or stories. But in this instance I feel it necessary to. Yes I had a meeting Celebs Go Dating after Caroline and I had separated. However, this was wrong.
“When someone has no money and nothing to lose they tend to do crazy irrational things.
“I am ashamed and trying to move on with my life. Please would you respect mine and Caroline’s privacy and not try and speculate on who said or did what.”
Flack and Brady met in January following his stint on Celebrity Big Brother and became engaged after just a few months.
The Love Island host – who has Brady’s initials tattooed on her arm – recently opened up about the start of their romance, telling fans in an open letter that she “followed” him on Instagram.
Writing in Cosmopolitan, she said: “I saw you on TV before we’d even met. ‘WHO is that guy?’ I texted my friend. ‘Oh, some man who was on The Apprentice, I think,’ she replied.
“I followed you on Instagram and you followed me back with the simple, emotionless line: ‘Thanks for the support.’ (I now know, of course, it took you hours to come up with that!).
“It made me laugh so I gave you my number. A few days later, we met.”