The customers who had been overcharged would be refunded.
Flack said she had called the company four times in the past fortnight, but was yet to receive her refund.
Netflix staff also failed to tell Flack how long it would take them to issue the refund, she said.
"I'm pretty unimpressed. It's put us into overdraft so there's the bank fees and all the rest of it.
"I'm a bit p***ed off to be honest."
She feared other Netflix users may have been overcharged without realising it if they did not check their bank statements.
"I worry that there's people being billed who don't know that extra money has gone out of their account."
Flack said she wanted to cancel her Netflix account after the experience.
"I'll wait until this issue's resolved but I don't think I'd be giving them my business in the future."
Netflix apologised to customers for a similar error in May last year, tweeting: "Sorry for the now resolved billing issues".
Several customers posted complaints on the company's social media accounts.
One user said they were billed 11 times.