The phrase "almost walked out" is correct and usable in written English.
It can be used to describe a situation where someone nearly left a place or situation but ultimately did not.
Example: "During the meeting, I almost walked out when the discussion turned heated."
Alternatives: "nearly left" or "was about to exit".
One of Joan Mondale's secretaries kept screaming during the sound check: "Oh, this is horrible, this is much too loud, you have to turn the volume down". The band almost walked out on the gig, but opted to turn down for the sound check.
Hibernian full-back Matt Doherty admits he almost walked out on the club in a difficult first couple of weeks of his loan period from Wolves before cementing his place in the team.
She almost walked out, but didn't.
The tennis champion who never threw in the towel almost walked out on the defining match of his career.
At a meeting two weeks ago Wednesday they almost walked out right then". Sgt. Mike Hadley, association president, charged that City Council members "have got their heads in the sand" and are ignoring the city's own survey of 11 area cities that showed Downey police officers were next-to-last in salary for veteran officers.
In addition, Donilon, who previously worked as a vice president for floundering mortgage giant Fannie Mae and was known for his strong views and opinions, once offending Defense Secretary Robert Gates so much during a meeting that the Pentagon chief almost walked out, according to Woodward.
Seamlessly forming a bridging point between old indie and 1960s pop, the band's new album Those The Brokes continues to unfailingly dispense the kind of easy-on-the-ears, middle-of-the-road rock which almost walks out of the shop on its own.
Edward lets Vivian almost walk out of his life, then he goes to get her in a grand romantic gesture.
Yolanda Martínez, 25, who had been in jail for almost seven years, walked out with her fist raised.
The single Keep It Part Two (Inferioty Part 1) failed to even reach the Top 75, and then almost the entire band walked out on him.
But my friends and colleagues were so warm, and there was such generosity in the ale-tinged air, that later I found myself involuntarily bleating 'I love you guys' as I walked out, almost sober, to my Uber".
