Flynn, who was previously forced to resign as the head of Defence Intelligence Agency, stands accused of discussing the lifting of sanctions on Moscow with the Russian ambassador in Washington before Mr Trump had taken office, an act which may be illegal.
The White House previously said he had contacted the ambassador in December for a Christmas greeting, but this account was challenged by recordings of the conversation by an intelligence agency.
Sally Yates, the then-acting US attorney general, told the White House late last month she believed Flynn had misled them about the nature of his communications with the Russian ambassador, current and former US officials told the Washington Post on Monday.
She said Flynn might have put himself into a compromising position, possibly leaving himself vulnerable to blackmail, the officials said. Yates was later fired for opposing Mr Trump's temporary entry ban for people from seven mostly Muslim nations.
Flynn had told Pence he had not discussed US sanctions against Russia with Russian officials in the weeks before Trump took office on January 20, prompting Pence to defend him in subsequent television interviews.
In recent days, Flynn has acknowledged he might have discussed sanctions with the Russians but could not remember with 100 percent certainty, which officials said had upset Pence, who felt he had been misled.
The FBI has been examining Flynn's phone calls amid questions about his interactions with Russian officials. In addition, the Army has been investigating whether Flynn received money from the Russian government during a trip he took to Moscow in 2015, two defence officials told the New York Times.
The NSC has traditionally brought together the expertise from intelligence world, the state department and defence agencies, advising the president on everything from counter-terrorism and foreign policy to nuclear deterrence.
But in the first three weeks of the new office, professional staffers have found themselves largely shut out of the West Wing, with decisions being made without adhering to the normal protocol for developing strategy.
Sources who asked not to be named for fear of retribution, told The Telegraph they worried that the White House's impatience with bureaucracy was part of a wider disregard for the institutions that underlie a functioning democracy.
At a recent meeting with NSC civil servants, sources said Flynn reportedly answered a question relating these concerns saying that having won the election this was the White House's prerogative.
Trump's decision to include Steve Bannon, his chief strategist as a decision maker in NSC meetings has also been seen as a dangerous break with a US tradition in which political operatives are kept out of decisions that are critical to national security.
Some members of staff are so concerned at what they fear are authoritarian trends that they bitterly refer to the new administration as "the regime".
The depth of Trump's break from tradition was made evident today as it emerged that he had responded to the news this weekend that North Korea had just test-fired a ballistic missile from his dinner table in a public setting.
Trump had been dining with Shinzo Abe, the Japanese prime minister, at his Mar-a-Lago club - nicknamed his Winter White House - surrounded by club members, and turned the table into a sort of open-air situation room.
Aides surrounded the leaders, and used flashlights on their mobile forms to shine light on maps and documents that were laid out over the silverware, CNN reported.
Members of the private club - whose fee was doubled to US$200,000 after Trump became president - posted incredulous pictures of the event.
Richard DeAgazio, a businessman, posted on his Facebook a picture of a man carrying the president's emergency satchel which he said called the "nuclear football", and claimed it contained the technology to launch a nuclear attack.
Security experts have said this casual approach to national security discussions was very risky, with some suggesting foreign powers could have hacked the phone's cameras.
Interviewing more than two dozen civil servants on the frustrations felt by NSC, the New York Times reported that many staff are kept in the dark about the substance of Trump's calls with foreign leaders. Civil servants are said to spend their time trying to discern his policy priorities from his tweets.
The policy papers that do reach the president's desk have reportedly been shortened from the three to six page reports preferred by Obama to a single page with lots of graphics. An aide is quoted as saying that "the president likes maps".
Similar concerns have been voiced by staffers at other departments. Sources at the state department say their research papers, even on matters as complex and critical as the fight against Isil in Iraq and Syria are going largely disregarded.
With every change of administration there is always a transition period at the NSC, whose staff is drawn from the Pentagon and other agencies, as the new president sets their priorities.
But Washington experts say that on this occasion a larger number of staffers than usual have left in protest, and the mutual mistrust is so deep that top advisers are reportedly considering monitoring staff mobile phones as they searches for the sources of numerous leaks.
Flynn is said to have furthered the practice of shutting out career civil servants, relying instead on some hand picked aides, according to Politico.
This article was originally published by Daily Telegraph UK.