From left, former chief of staff Donald Rumsfeld, Betty Ford and Dick Cheney (David Hume Kennerly)

“When anybody gives you advice about, ‘Oh you should do this, you should do that’ — unless they’ve sat in that cockpit seat and been strafed by friendly fire as well as enemy fire, they don’t know anything about the job,” former Obama White House chief of staff Rahm Emanuel insists in “The Gatekeepers,” a multi-episode special on chiefs of staff over the years.

The special, which Discovery Channel will premiere next year, spans nine administrations, with interviews from more than a dozen former chiefs of staff (a more powerful job than vice president, says Dick Cheney — who’s been both — in the series). The list of those who agreed to sit with the exec producers includes not only Emanuel and Cheney, but also Donald Rumsfeld, James A. Baker III, John Sununu and Thomas F. “Mack” McLarty, as well as former presidents Jimmy Carter and George H.W. Bush.

The project is the brainchild of brothers Gedeon and Jules Naudet, filmmakers made famous when their work on a documentary about firefighters in Lower Manhattan put them at the World Trade Center on Sept. 11, 2001. The results of that dramatic coincidence became the riveting CBS News documentary “9/11,” which was showered with awards — including an Emmy (outstanding nonfiction special) and a Peabody, a Writers Guild of America Award, the Radio Television News Directors Association’s Edward R. Murrow Award and a Television Critics Association Award, among many other accolades.

“We had been fans of ‘The West Wing’ and love that character,” Jules Naudet told The TV Column, regarding the beloved Leo McGarry role played by the late John Spencer in the hit NBC drama that put the White House through the Aaron Sorkin Filter.

“A lot of people know about the president and vice president, but the chief of staff — that’s a very strange, secret brotherhood no one knows about,” said Naudet — and that fact, Rumsfeld told the filmmakers, “is a good thing.”

The Naudets, in turn, brought in exec producer and longtime news exec Chris Whipple (“60 Minutes,” ABC News), who conducted many of the interviews. And Pulitzer Prize-winning White House photographer David Hume Kennerly was brought in as producer.

Discovery Channel will unveil the resulting multi-episode series during its “upfront” presentation to advertisers next week in New York. The network promises it will detail how two Reagan chiefs of staff, Baker and Ken Duberstein, handled the demands of Nancy Reagan’s astrologer; which 25-year-old chief of staff was put in charge of reviewing J. Edgar Hoover’s infamous FBI files before forwarding them to the president; and whether Carter believes he could have avoided the disastrous mission to rescue the American hostages in Iran, if only he’d asked his chief of staff Jack Watson. (Spoiler alert: no.)

(Discovery, BTW, seems to be doing more history projects than a cable network called History these days, including the recently announced Amelia Earhart Project, in which Discovery will attempt to recover the wreckage of the famed aviator’s plane; she went down on the last leg of a round-the-world trip 75 years ago.)

Anyway, getting back to “Gatekeepers”:

Whipple and Jules Naudet said they were surprised at how forthcoming all the men were, although an 11-minute sizzle reel shown to The TV Column was more gate-keeping than eye-opening. (Sample: “The White House chief of staff is one person besides his wife who can do that,” Rumsfeld says, “who can look [the president] right in the eye and say: ‘This is not right. You simply can’t go down that road. . . . It’s a mistake.’ ”)

But, Whipple and Naudet explained, they’re saving the best bits for the telecast. Fair enough. So you’ll have to wait for the premiere next calendar year to learn what Rumsfeld and Cheney told them about the Obama administration’s having successfully knocked off Osama bin Laden.

We, however, did get to see what Carter had to say about it.

Carter is seen trying to salvage something from the botched rescue mission during his administration, suggesting his mistake helped inform Obama’s campaign to kill bin Laden. (We already know it served as a cautionary tale as to how it could end a presidency.)

We also got to hear Carter’s chief of staff, Watson, say: “Had I known about [the rescue mission], I would have said to the president, ‘Flying helicopters at low altitudes over vast stretches of desert is a formula for disaster.’ ”

And what did Carter think about that? Not much: “Whether Jack Watson had been in that meeting or not would have had no impact on my decision to go ahead. In fact, everybody in that meeting agreed we should go.”

Whipple did volunteer that, during his interview, Baker told them that when Reagan took office, he wanted to reform Social Security. Baker took Reagan aside and said, “Mr. President, Social Security is the third rail of American politics. If you touch it, you will be electrocuted.”

“And lo and behold, what did Reagan decide to pursue, which became his legacy? Tax cuts. Baker really turned him around on that,” Whipple concluded.

Cheney, who was interviewed twice for the special, told them he has forgotten a lot of the stuff he did as vice president, but remembers everything he did as a 30-something chief of staff for Gerald Ford. “It was probably his favorite job of all the jobs he’s had,” Whipple said.

And the job Cheney blames for his first heart attack, according to his interview.

Some of the men stipulated that they could be asked only about their time as chief of staff and not other political roles they’ve played, Whipple explained. Cheney, though, seemed to forget those ground rules during the course of his interviews. And Emanuel — the series’ only former chief of staff to a sitting president — focused more on the personal aspects of the job.

In one of the most Aaron Sorkin-ish chapters in the making of “Gatekeepers,” Whipple described how some of the men spoke about a cold December morning in 2008 when 13 of the living chiefs of staff gathered in the COS office in the West Wing to meet Emanuel at a time when “all hell was breaking loose, the economy was in a free fall, two wars raging and the auto industry was collapsing. All of these guys came together . . . to give Rahm Emanuel advice.”

After each member of this “elite fraternity of Washington insiders” had his crack at imparting wisdom to Emanuel, it was Cheney’s turn. “And Cheney looks Rahm in the eye and says, ‘At all costs, control your vice president.’ Of course, Cheney was the sitting vice president and obviously knew that everybody thought he was running the Bush White House. It brought the house down — everyone cracked up,” Whipple chuckled.

“The chief of staff is confessor and consigliore to the president, Whipple argued. “You really can make the argument that he really makes the difference between success and failure for every president.”

Indeed, several of the men were seen in the 11-minute trailer explaining that during their watch, the position was second only to POTUS, and that they were, as the show’s title suggests, gatekeepers to the most powerful man in the free world.

Hooey, said Barbara Bush during her interview. “This is going to disappoint you terribly,” she is seen telling the producers as she fills the screen, all pearls and no nonsense. “But I never once called one of George’s chiefs of staff. Ever.

“If I had anything to say — I said it to George Bush.”