Representative Elijah Cummings, the House committee's top Democrat, released other Defence Department documents showing that the DIA found no evidence that Flynn requested permission to accept foreign funds, despite a 2014 warning against taking such payments.
In a letter sent to the acting secretary of the Army, Republican House Oversight Committee chairman Jason Chaffetz requested that "in light of these apparent violations" the Army establish a way for Mr Flynn to repay the hundred of thousands of dollars that he received from the governments of Russian Federation and Turkey.
Bruce Anderson, a spokesman for the Defense Department Inspector General, said Thursday that the investigation into Flynn began April 4.
"General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit", reads the statement, in part.
The letter explained such "advance approval" would need to come "from the relevant service secretary".
Last month, Flynn filed an amended disclosure of payments for speeches from three Russian-linked companies, including the state-backed network RT, without providing further records related to the payments.
Flynn has previously disclosed that he received between $50,000 and $100,000 as part of his personal stake in $530,000 that his company, Flynn Intel Group, received for consulting work performed previous year for a Turkish businessman.
The issue involving Turkey emerged after Flynn retroactively registered in March with the Justice Department as a foreign agent for work that his company, Flynn Intel Group, carried out on behalf of Inovo BV, a Netherlands-based company.
Army spokeswoman Cynthia O Smith said "we have found no records of LTG (R) Flynn requesting permission from the Army for foreign employment". Rep. Cummings, a Democrat, and Republican Congressman Jason Chaffetz each charged that Flynn may have broken the law in taking payments from foreign nations, reports Roll Call. Chaffetz, however, did not join Cummings at the Thursday news conference, unlike their bipartisan appearance earlier in the week announcing the results of the committee's inquiry into Flynn's dealings with authorities before and after his foreign earnings. Chaffetz also sent a letter Thursday to the acting secretary of the Army asking for a final determination as to whether Flynn violated the law.
During the 2016 campaign, Flynn emerged as a confidante and key advisor to then-candidate Donald Trump, who made a series of pronouncements on the campaign trail that broke with US policy and favored the Kremlin.
As congressional and FBI investigators probe the Trump campaign's relationship to Russian Federation in the aftermath of an election season that saw Kremlin agents attempt to boost the real estate mogul's electoral chances through a campaign of hacking and leaking sensitive documents, Flynn's work has emerged as one focus of the investigations.
Flynn resigned on February 13 after failing to disclose his talks with Sergei Kislyak, Russian ambassador to the United States, before Trump took office.
"These documents raise grave questions about why Gen. Flynn concealed the payments he received from foreign sources after he was warned explicitly by the Pentagon", Cummings said in a statement.
The investigation was revealed in documents released by the top Democrat on the House Oversight Committee Thursday morning.
What makes this entire situation even more unprecedented is the foot-dragging by President Donald Trump's administration regarding Flynn's behavior during his short stint in the White House.