The Pentagon office will try to determine whether Flynn "failed to obtain required approval prior to receiving" the payments, according to an April 11 letter from Defense Department Inspector General Glenn A. Fine to Rep. Jason Chaffetz (R. -Utah), the committee chairman.
Further, Cummings said there is no evidence Flynn did seek permission to receive payment from a foreign government, which contradicts what Flynn's lawyer has said.
The Democrats on the House Oversight Committee also sent a request to Chaffetz Thursday that they schedule a meeting with the White House to demand the release of the Flynn documents they have asked for.
Michael Flynn, seen here arriving for a news conference in the East Room of the White House in February, is being investigated by the inspector general of the Department of Defense, Rep. Elijah Cummings said Thursday.
Flynn was reportedly paid $45,000 from RT, according to CNBC. Cummings said no proof of that has been found. The letter stopped short of calling for a subpoena, demanding instead for "the Committee hold a meeting with White House officials to discuss the terms of the document production".
It could also extend to the $530,000 Mr Flynn was paid to lobby for Turkey during last year's presidential election campaign.
Michael Flynn, the former national security adviser. Flynn was pushed out of that job in 2014 and the DIA explicitly told Flynn that he could not to accept any compensation from a foreign state without prior permission from the federal government.
Flynn claims the DIA was briefed on the payment, but the information released by Cummings shows that the agency can not find any documentation "referring or relating" to his "receipt of money from a foreign source".
White House spokesman Sean Spicer told reporters on Thursday that the inspector general's probe was "appropriate".
Flynn earned tens of thousands of dollars from Russia's state-sponsored RT television network and from a Turkish businessman linked to Turkey's government. Flynn retroactively registered as a foreign lobbyist with the Department of Justice in March.
Flynn's attorney did not immediately respond to a request for comment. Failing to disclose foreign payments is a criminal offense that could lead to fines and jail time. He also received payments for additional speeches to Russian firms Kaspersky and Volga Dnepr. Chaffetz said he believes the administration simply does not possess the documents, while Cummings has said they are intentionally withholding information about Flynn.
After leaving the military, Flynn opened a government relations company and became a top adviser to the Trump campaign past year.
But in an unusual tangent after being asked whether Trump was "satisfied" with how Flynn - who was sacked as national security adviser in February after he lied to Vice President Pence about the nature of his discussions with the Russian ambassador before Trump was sworn in - had been vetted by the administration, Spicer signaled that the President's team never fully vetted the general because his security clearance had been renewed in 2016 when Barack Obama was still in office.