Michael Flynn quit following reports that he had misled Vice President Mike Pence and other officials about his contacts with Russia.
He had been embroiled in controversy since it was revealed that he had a conversation with a Russian diplomat about sanctions prior to the US President's administration taking office.
Shortly after his resignation Philippe Reines, a former aide to Ms Clinton tweeted about it.
“Dear Mike Flynn & Mike Flynn Jr. What goes around COMETS (sic) around," he said.
"And given your pizza obsession," he added, with link to a Domino's Pizza job link. He signed it off with "xo Philippe”.
Ms Clinton retweeted his message, adding one of her own.
She said: "Philippe's got his own way of saying things, but he has a point about the real consequences of fake news..."
Mr Reines appeared to be referencing a fake news story that emerged during the presidential election campaign, which accused her of running a child sex ring out of a Washington DC, pizza shop
The story was circulated by Mr Flynn’s son, Michael Flynn Jr, last December. at the time he was working for his father in the transition teambut lost his job over a tweet.
His father is also now out of a job.
In a resignation letter, Mr Flynn said he gave Vice President Mike Pence and others "incomplete information" about his calls with Russia's ambassador to the US.
The Vice President, apparently relying on information from Mr Flynn, initially said the national security adviser had not discussed sanctions with the Russian envoy, though Mr Flynn later conceded the issue may have come up.
The controversial orders Donald Trump has already issued
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President Trump has named retired Lieutenant General Keith Kellogg as the acting national security adviser.
He had previously been appointed the National Security Council chief of staff and advised Mr Trump during the campaign.
The President is also considering former CIA Director David Petraeus and Vice Admiral Robert Harward, a US Navy SEAL, for the post, according to a senior administration official.
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