The Constitution's Emoluments Clause which has been raised as an issue with President Donald Trump's business dealings forbids a public official from receiving payment from foreign governments, and Chaffetz says that applies to retired military generals. Flynn is a retired Army lieutenant general.
Flynn attended a gala celebrating RT's 10th anniversary and sat next to Russian President Vladimir Putin.
Chaffetz's letter to Leading Authorities Inc. CEO Mark French seeks Flynn's contract with the speaker's bureau and documents related to that RT speech and any others with ties to the Russian government as well as a list of all speeches and payments.
The Defense Department told the Oversight Committee that it has no records of requests to approve such a payment from a foreign entity, the committee said.
Trump also said Thursday that he had called the Justice Department asking for a probe into the intelligence leaks after blaming them on holdovers from President Barack Obama's administration. He also slammed the news media for covering the story that led to Flynn's ouster.
"The press should be ashamed of themselves," Trump said at a news conference. "More importantly, the people who gave out this information should be ashamed of themselves."
Chaffetz's letter, co-signed by Rep. Bob Goodlatte, R-Va., chairman of the House Judiciary Committee, asks the Justice Department's inspector general to immediately look into possible mishandling of classified information.
"We have serious concerns about the potential inadequate protection of classified information here," Chaffetz and Goodlatte wrote.
Democrats have urged Chaffetz to use his authority as Oversight chairman to open more investigations, specifically into what ties Trump's campaign has to Russia and what conversations occurred during the election.
U.S. intelligence agencies found that Russia had attempted to sway the election in Trump's favor, a point that Trump's team has disputed.
Cummings, the top Democrat on the Oversight Committee, responded to Chaffetz's letter seeking a probe of intelligence leaks by saying that the Utah Republican "appears to be taking his marching orders" directly from Trump by focusing on the leaks and not on Flynn's lies to Vice President Mike Pence and the American people.
"Congress should be doing independent oversight of the executive branch and protecting whistleblowers, not running interference while the White House conceals their abuses and misleads the American people for weeks," Cummings said. "Chairman Chaffetz said he didn't want to go on 'fishing expeditions,' but that's exactly what he's doing here."