The United States-listed firm wants to stop the 21-year-old from using its trademarked product name as a moniker in advertisements for tennis clothing, a spokeswoman told Reuters.
The matter had its first hearing in Federal Court of the city of Adelaide, Kokkinakis's hometown, on Thursday, according to court filings.
Kellogg's lawyer declined to comment, while Kokkinakis's lawyer did not respond to two calls requesting comment.
The tennis player's official Twitter account on Thursday published a crying laughter image with no words.
Kellogg, which dominates the Australian cereal market, promotes Special K as a healthy, low-fat, low-sugar breakfast, often featuring physical activity in its advertisements.
"His association (with the brand) could help, but at the end of the day it's a trademark that we own and we want to continue to own," said the Kellogg spokeswoman, referring to Kokkinakis.
The Davis Cup player reached his highest world ranking of 69 as a teenager in 2015 before a series of injuries sidelined him for the best part of 18 months. He made his singles return in Bordeaux last month.
(Editing by Byron Kaye and Sudipto Ganguly)
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