Ms Flint made the allegation on Sky News' Sophy Ridge On Sunday programme after losing her seat at the General Election.
She claimed Ms Thornberry had told a colleague: "I'm glad my constituents aren't as stupid as yours."
She said: "Keir Starmer led us to a policy that did not listen to Labour Leave voices who urged caution, he led us down the path of a second referendum, and I'm afraid Emily Thornberry did as well - she said to one of my colleagues, 'I'm glad my constituents aren't as stupid as yours'."
Ms Thornberry, the Islington South and Finsbury MP, said the quote attributed to her "is a total and utter lie".
"I've never said that to anyone, nor anything like it, nor would I ever think it," she added.
"Whatever our differences, let's not sink into that gutter."
And she told Sky News today: "One of my former colleagues came out and said the most extraordinary lies about me.
"I've contacted her and I've said to her, 'Please withdraw, I will give you until the end of the day' and she hasn't.
"So I've had to go to solicitors. I mean, people can slag me off - so long as it is true, I'll take it on the chin.
"But they can't make up s*** about me and, if they do, I have to take it to the courts."
However Ms Flint stood by her comments and told Piers Morgan on ITV's Good Morning Britain: "I stand by my comments yesterday but I don't want to comment any further because there may be legal proceedings but I said what I said and I stand by them."