Kelly, a former Navy pilot, is seeking to block his censure from Defense Secretary Pete Hegseth last week.
Hegseth announced last Monday that he censured Kelly over the Arizona Democrat's participation in a video that called on troops to resist unlawful orders.
"The First Amendment forbids the government and its officials from punishing disfavored expression or retaliating against protected speech," his lawsuit says.
"That prohibition applies with particular force to legislators speaking on matters of public policy."Hegseth said the censure — by itself simply a formal letter with little practical consequence — was "a necessary process step" to proceedings that could result in a demotion from Kelly's retired rank of captain and subsequent reduction in retirement pay.