Flynn, who is believed to have provided substantial evidence in the case, is due to be sentenced Tuesday after pleading guilty past year to one count of making false statements - a charge brought by Robert Mueller, the special counsel investigating Russia's interference in the 2016 United States presidential election.
The case sheds further light on how Flynn and those around him worked to benefit a foreign country in the months before he became one of America's top national security officials.
The indictment notes that Kian was vice chairman of Flynn's business group, the Flynn Intel Group. The Turkish leader blames Gulen for a failed military coup that sought to oust the Turkish leader in the summer of 2016, and has launched a widespread purge of any members of the Turkish civil service who he believes support Gulen.
Mr Flynn, who is due to be sentenced on Tuesday (local time) for lying to the Federal Bureau of Investigation in relation to his contacts with the then-Russian ambassador to the United States, Sergei Kislyak, has also admitted to lying about his role in the Turkish lobbying effort and has been cooperating with prosecutors on the probe.
Alptekin is also charged with failing to register as a foreign agent and also making false statements.
A senior White official pushed back on that assertion on Monday, stressing that Trump did not commit during a meeting with Erdogan at the G20 summit two weeks ago to extradite Gulen, who denies involvement in the coup attempt.
Flynn served as Donald Trump's national security adviser in the first weeks of his presidency
Mr Rafiekian was a former director at the US Export-Import Bank and a co-founder of the Flynn Intel Group (FIG), the consultancy at the heart of the case.
That same month, according to the indictment, Flynn, Kian, and Alptekin met with high-level Turkish officials in NY to discuss the campaign.
In the summer of 2016, when Flynn was working as an adviser to the Trump campaign, the three initiated what they called a "Truth Campaign" that compared Gulen to Iran's Ayatollah Khomeini.
Kian and Alptekin are each charged with conspiracy and acting in the United States as an illegal agent of the government of Turkey.
Of the roughly $600,000 paid to Mr Flynn's company, $80,000 was sent back to Mr Alptekin through his Netherlands-based firm Inovo BV, Justice Department filings show. According to the indictment, Alptekin worked at the direction of the Turkish government, but the defendants worked to hide that fact.
Flynn is set to be sentenced Tuesday for lying to FBI agents as part of a special counsel investigation of Russian interference in the 2016 presidential campaign.
U.S. media say this may possibly be due to Flynn's cooperation in the Russian Federation probe by Special Counsel Robert Mueller.
Flynn was charged by Mueller for lying to investigators past year, including about his work at the Flynn Intel Group Inc. on behalf of Turkey.