Flynn traveled to Moscow in December 2015 to give an address for the network's tenth anniversary gala, The Daily Beast wrote.
Months later Flynn joined Donald Trump's presidential campaign as an adviser and was served briefly as National Security Adviser before he was fired in February.
The Republican chairman of the committee, Rep. Jason Chaffetz, asked the Army to issue a final determination on whether Flynn had illegally failed to disclose the RT payment, citing the documents released on Thursday.
Read alsoTrump's ex-adviser paid by Russia propagandist RT, Kaspersky Lab – media"By all appearances, Lt. Gen. Flynn violated [federal law] by accepting compensation from entities associated with foreign governments without obtaining consent to do so," Chaffetz wrote.
Financial disclosure documents released by the White House early this month showed that Flynn had initially failed to inform federal ethics officials of the payment after taking his White House post.
If he also failed to inform DIA of that payment, Flynn likely ran afoul of federal laws requiring former government officials to seek approval from the State Department and the agencies that once employed them before accepting a payment from a foreign government.
"These documents raise grave questions about why General Flynn concealed the payments he received from foreign sources after he was warned explicitly by the Pentagon," Rep. Elijah Cummings, the top Democrat on the House Oversight Committee, said in a Thursday statement.
Flynn's attorney Rob Kelner said this week that Flynn had informed DIA that he would travel to Moscow for the RT event, but would not say whether he had disclosed his payment for speaking at it.
In an emailed statement Kelner disputed Cummings' characterization of DIA's letter, saying it was actually exculpatory.
"DIA's letter actually confirms, in a terse section that is partly redacted, that General Flynn provided information and documents on a thumb drive to the Department of Defense concerning the RT speaking event in Moscow, including documents reflecting that he was using a speakers bureau for the event," Kelner wrote. "We urge DIA and the Committee to release the full, unredacted letter, along with the documents that General Flynn provided to DIA during the briefings and details concerning the in-person briefings provided by General Flynn to DIA."
The versions of the documents that were released on Thursday show that DIA has no record of Flynn's payment from a Russian government-linked entity.
Flynn's foreign payments are currently the subject of an investigation by the Pentagon's inspector general, according to additional documents released by the oversight committee.