The inspector general is probing whether Mr Flynn had "failed to obtain required approval prior to receiving any emolument from a foreign government," according to the April 11 letter to the House Oversight and Government Reform Committee.
Mr Flynn is under scrutiny over his contacts with Russian officials, and lawmakers have said he likely broke the law by failing to request and receive permission to accept payments for a 2015 trip to Russia.
Representative Elijah Cummings, the top Democrat on the House Committee on Oversight and Government Reform, also released documents from the Pentagon that showed it had found no evidence that Mr Flynn sought permission to receive foreign funds despite being warned in 2014 against taking such payments.
An attorney for Mr Flynn did not immediately respond to a request for comment.
In a redacted version of a letter sent to the committee this week, the Defense Intelligence Agency (DIA) told lawmakers it had found no evidence that Mr Flynn sought approval of or reported any foreign payments.
Cummings also released an October 2014 letter from DIA to Mr Flynn outlining ethics restrictions that applied to him on retirement from the US Army, including a prohibition on accepting payments from foreign sources without permission.
The latest release of documents comes amid congressional investigations of possible ties between Mr Trump's election campaign and Russia.
Mr Flynn resigned on February 13 after failing to disclose his talks with Sergei Kislyak, Russian ambassador to the United States, before Mr Trump took office.
(Reporting by Susan Heavey and David Alexander, Editing by Jeffrey Benkoe)