Reps. Jason Chaffetz (R-Utah) and Elijah Cummings (D-Md.), the top lawmakers on the committee, told reporters on Tuesday that Flynn inappropriately received almost $34,000 for a 2015 speech in Moscow for the Russian propaganda outlet RT.
"No former military officer is allowed to accept payments from a foreign government, and my guess is this is probably not the first time this has happened", he added.
"The White House refused to provide the committee with a single piece of paper in response to our bipartisan requests", he said. The section reads: "No title of nobility shall be granted by the United States: And no person holding any office of profit or trust under them, shall, without the consent of the Congress, accept of any present, emolument, office, or title, of any kind whatever, from any king, prince, or foreign state".
The White House says it is "unclear" how their request for contacts and communications between Michael Flynn and foreign nationals after the inauguration is "relevant to the stated objective of the Committee's review, which according to your letter is to examine Lt. Gen. Flynn's disclosure of payments".
Representative Elijah Cummings of Maryland, the committee's ranking Democrat, said Flynn's contacts were "a major problem". The House Intelligence Committee has also invited Yates and Clapper to testify in a public hearing that has not yet been scheduled. RT paid Leading Authorities, a private firm that arranges for speakers for events, according to the Yale Journal on Regulation. For his work lobbying on behalf of the Turkish Government, he was paid more than US$500,000.
"I see no data to support the notion that General Flynn complied with the law", said the Republican chairman of the committee, Jason Chaffetz.
"The statute's real clear". "He was supposed to get permission, he was supposed to report it, and he didn't. But it appears as if he didn't even try to do that and jump over that bar".
Cummings also raised the specter of a crime, noting that concealing payments from the USA government would be a felony punishable by five years in jail.
Cummings said the committee had asked the White House, in which Flynn served as President Donald Trump's national security adviser for less than a month, for more information about his financial disclosures. The committee made six requests, and the White House cited reasons it could not comply with each of them. Some Democrats believe the White House wants to limit what Yates says publicly, but the White House has denied this.
Asked whether Flynn had violated federal law, Spicer told reporters Tuesday, "That would be a question for him".
In a statement from his attorney, Flynn said he made proper disclosures before taking the job as Trump's national security adviser.
Flynn, who headed the military's top intelligence agency, was sacked as Trump's national security adviser in February over misleading comments he made to the vice president about his discussions with the Russian ambassador during the transition.
Then-Deputy Attorney General Sally Yates spoke during a June 28 news conference at the Justice Department in Washington.
A Democratic member of the House Oversight Committee called for "an independent, 9/11 style commission" into possible ties between the Trump campaign and Russian Federation.
On May 8, a public hearing will be held before the Senate Judiciary subcommittee.
Flynn campaigned vigorously for Trump before the presidential election and was chosen as national security adviser in January.
U.S. intelligence agencies have found that Russian Federation hacked into Democratic emails and leaked them a year ago in an effort to hurt Democratic candidate Hillary Clinton and ultimately to help elect Trump.
Ms Yates' testimony will mark her first appearance on Capitol Hill since she was sacked in late January after refusing to defend President Trump's travel ban on certain foreigners.