Davis had called the method to decide the role "dishonourable" in a tweet on Thursday when Luger Erin Hamlin was selected to carry the flag instead.
A U.S. speed skating spokesman said Davis had not originally planned to march in the parade of nations later on Friday, but would have made an exception if he had been chosen as flag-bearer.
"Shani won't march in the parade. It was never part of his plans. He is fully focused on his first race and is concentrating on that," the spokesman said.
Davis, who qualified for his fifth Olympics in South Korea, was one of eight athletes in contention to carry the flag, but lost out to Hamlin.
The flag-bearer is chosen by a vote of the eight U.S. winter sports federations but the vote was tied 4-4 between Hamlin and Davis, and a coin was used to break the tie, in keeping with USOC rules.
In his tweet, Davis added the hashtag "BlackHistoryMonth2018", suggesting racial bias was involved.
"I am an American and when I won the 1000m in 2010 I became the first American to 2-peat in that event," Davis tweeted shortly after the United States Olympic Committee (USOC) announced its decision on Thursday.
"@TeamUSA dishonorably tossed a coin to decide its 2018 flag bearer. No problem. I can wait until 2022. #BlackHistoryMonth2018 #PyeongChang2018."
Davis, who has won two Olympic golds and two silvers, became the first black athlete to claim an individual Winter Olympics gold medal in 2006.
The 35-year-old declined to comment on his social media outburst after a training session at the Gangneung Oval on Friday.
Hamlin, who will retire after the Games and became the first American female luger to medal at an Olympics when she won bronze in Sochi four years, said she was "honoured and excited" to be named flag-bearer.
"This is something totally different (than winning an Olympic medal)," the 31-year-old said in a statement.
"It's something that is because of that hard work. People acknowledge that and respect that. It's a big privilege to represent Team USA."
(Editing by John O'Brien)
