The ousting of Flavel is one of the first actions taken by NatWest's interim CEO Paul Thwaite, after the group's former CEO Alison Rose quit on Wednesday over the same matter.
Flavel said the handling of the case had "fallen below the bank's high standards of personal service".
NatWest has faced intense scrutiny over the decision by Coutts to sever ties with Farage.
An internal review obtained by the politician-turned-TV show host showed Coutts' wealth reputational risk committee had said his values did not align with the bank's own.
Rose left after she admitted she'd discussed details about the accounts with a BBC journalist. The public broadcaster later ran a story suggesting Farage's services had been axed because he wasn't wealthy enough, a report it later said was incomplete and inaccurate.
The review published by Farage showed his political views were a factor in the decision to cut him, alongside commercial considerations. He was offered a standard NatWest account instead.
NatWest's board has also come under pressure from investors over its handling of the fiasco, after giving Rose its "full confidence" on Tuesday evening only for her to leave hours later.
Writing on social media platform X, formerly Twitter, Farage said it had only been a "matter of time" before Flavel stood down, adding that he had written to him twice before speaking publicly about his case and not received an acknowledgement.
One of NatWest's 20 largest shareholders told Reuters that chairman Howard Davies' position was looking increasingly shaky, echoing other media reports.
A spokesperson for the bank declined to comment on the chairman's position.
Shares in the bank were trading 1% lower at 1324 GMT, against a 0.3% rise in the FTSE 100.
Australian-born Flavel, who previously served as CEO of JPMorgan Private Wealth Management in Asia Pacific region, took the top job at Coutts in 2016.
During his tenure at the 330 year-old lender, which has banked Britons from Charles Dickens to Queen Elizabeth II, Flavel tried to update its technology and court younger wealthy clients.
Mohammad Kamal Syed will step into the role of interim CEO of Coutts and NatWest's wealth businesses, Thwaite said, adding that Flavel was stepping down by "mutual consent".
