Among other things, Ms. Powell asked for material that appeared to be based on claims about the Russia investigation that have circulated in the conservative media without evidence to back them up. For example, she suggested that a former top F.B.I. official, Andrew G. McCabe, declared that the bureau would go after Mr. Flynn and then Mr. Trump. (Prosecutors said they had disproved the allegation, which an agent called “ludicrous.”)

One by one, Judge Sullivan rejected her assertions.

For instance, she wrote that the government suppressed evidence favorable to Mr. Flynn related to agents’ questioning of him. “High-ranking F.B.I. officials orchestrated an ambush interview,” Mr. Flynn’s lawyers wrote in court documents, saying they were “trapping him into making false statements they could allege as false.”

Judge Sullivan dismissed that accusation, citing agents’ notes and F.B.I. memos known as 302s documenting their interview of Mr. Flynn. The documents were “both consistent and clear that Mr. Flynn made false statements to the F.B.I.,” Judge Sullivan wrote.

In other requests, Mr. Flynn’s lawyers sought material that they already had or that seemingly had little or nothing to do with his case. Judge Sullivan sided with prosecutors who said in several instances that Mr. Flynn’s lawyers wanted information that would not help their client. “By any conceivable measure, Mr. Flynn’s requested information is neither helpful nor relevant to the defense,” the judge wrote.