The Pentagon hasn’t found any documents indicating that Mike Flynn received authorization to accept money from a foreign government before traveling to Moscow in 2015 for a paid Russian state TV event, according to a letter from the acting Secretary of the Army.

The Pentagon finding came after lawmakers raised questions about whether the former White House national security adviser and retired U.S. Army general violated Pentagon rules that require retired officers to report income from foreign states.

Mr. Flynn accepted an invitation to Moscow in late 2015 to give a paid, sit-down interview with Russian state television network RT and to attend the channel’s 10-year anniversary gala, where he sat beside President Vladimir Putin.

The Department of the Army conducted “a thorough records search, and has not found any documents,” Acting Secretary of the Army Robert Speer said in a Feb. 14 letter in response to Rep. Elijah Cummings, a ranking Democrat on the House Oversight Committee, who asked the Pentagon whether Mr. Flynn received approval. Several Democratic lawmakers recently asked the Defense Department to investigate whether Mr. Flynn violated the Constitution when he accepted money for attending the Russian network’s event.

Mr. Flynn previously said he was paid to attend the December 2015 event, which came at a time of heightened tensions between the White House and the Kremlin. In an interview with the Washington Post in August, Mr. Flynn said he was asked to attend the event by his speaking-engagement agent, Leading Authorities Inc., or LAI.

“It was in Russia. It was a paid speaking opportunity,” Mr. Flynn said. “I get paid so much. The speaker’s bureau got paid so much, based on our contract.”

On Thursday, Mr. Cummings, of Maryland, sent a joint letter with the committee chairman, Rep. Jason Chaffetz (R., Utah), asking LAI to provide documents and information on the matter by March 2.

In particular, they asked LAI for all documents and communications relating to Mr. Flynn’s December 2015 appearance in Moscow and the source of the funding for the trip. They also asked for a list of all of Mr. Flynn’s speaking engagements and their sources of funding.

“We are attempting to determine the amount Lt. Gen. Flynn received for his appearance, the source of the funding, and whether he may have received payments from any other foreign sources for additional engagements,” the congressmen wrote in the letter.

As chairman of the committee, Mr. Chaffetz has subpoena power that could compel LAI to hand over the information. LAI didn’t respond to requests for comment.