Although he served two tours in Washington as a Marine general, he never quite became a political operator in the manner of Gen. Colin Powell or Gen. David Petraeus.
To appoint Kelly, the former Homeland Security secretary, as his chief of staff, is a huge gamble, but in keeping with Trump's style.
Kelly formerly commanded coalition troops in Iraq from 2008 to 2009.
But perhaps that is not even what Trump, who seems to thrive on constant upheaval, wants.
Priebus was head of the Republican National Committee before joining the White House as chief of staff.
Scaramucci in subsequent television interviews said he wasn't sure if his spat with Priebus over leaks "is reparable or not, that will be up to the president".
For one thing, Priebus was among the advisers who had to persuade Trump not to drop out of the presidential debates. By ordinary standards, Spicer and Priebus have been far too loyal to Trump for far too long - to their own detriment.
Mr Trump has said he is "very disappointed" in Mr Sessions and was "looking" at firing him. Such a definition of loyalty is ultimately impossible to reconcile with an administration governed by laws rather than personal bonds.
Priebus resigned privately Thursday, according to media reports.
Who's who in the Anthony Scaramucci White House spat?
A string of firings and resignations has at times made Donald's Trump White House resemble the reality TV show he once hosted.
Outgoing White House Press Secretary Sean Spicer was seen on the premises of his old work place on Saturday.
The biggest target of Scaramucci's attack: Reince Priebus.
He took the job, he says, because it fit his background, and he threw himself into his new role with rigor, earning him the highest compliment from the commander in chief, who called him a "tough guy". Priebus, he said, "knows better than to lecture me".
Priebus, whose departure was the latest in a string of early exits from the administration, also was blamed by some within the White House for the failure of the Republican health care plan, with some Trump allies believing that Priebus' longtime relationships with Republicans on Capitol Hill should have ensured the bill's passage.
When Trump asked him to join his administration as secretary of Homeland Security, he "panicked for a bit", he told the Aspen Security Conference last week: "All I could think about is, how do I get out of this?"