The phrase men in buckram denotes imaginary or non-existent people.

This phrase alludes to John Falstaff’s vaunting tale (in which two men in buckram suits gradually become eleven) in The History of Henrie the Fourth; With the battell at Shrewsburie, betweene the King and Lord Henry Percy, surnamed Henrie Hotspur of the North, With the humorous conceits of Sir Iohn Falstalffe (London: Printed by P.S. for Andrew Wise […], 1598), by the English poet and playwright William Shakespeare (1564-1616):
—Context: Falstaff tells Poins and Prince Harry, nicknamed Hal, how he was robbed just after committing his own robbery. In fact, Falstaff was attacked and robbed by Poins and Hal themselves, in disguise. They played this trick on Falstaff to hear the lies that he would later tell to try to justify himself:

Falst. I haue pepperd two of them.
Two I am sure I haue paied, two rogues in buckrom sutes: I tel
thee what Hall, if I tell thee a lie, spit in my face; call me horse,
thou knowest my olde warde: here I lay, and thus I bore my
poynt, foure rogues in Buckrom let driue at me.
Prin What foure? thou saidst but two euen now.
Falst. Foure Hal, I told thee foure.
Poin. I, I, he said foure.
Fal. These foure came all a front, and mainely thrust at me,
I made me no more adoe, but tooke all their seuen points in my
target, thus.
Prin. Seuen, why there were but foure euen now.
Falst. In Buckrom.
Po. I foure in Buckrom suites.
Falst. Seuen by these hilts, or I am a villaine else.
Pr. Preethe let him alone, we shall haue more anon.
Falst. Doest thou heare me Hal?
Prince. I, and marke thee to iacke.
Falst. Do so, for it is worth the listning to, these nine in Buck-
rom that I told thee of.
Prince. So, two more alreadie.
Falst. Their points being broken.
Poy. Downe fell their hose.
Falst. Began to giue me ground: but I followed me close, came
in, foot, and hand, and with a thought, seuen of the eleuen I paid.
Prin. O monstrous! eleuen Buckrom men growne out of two.

There have been many references to John Falstaff’s tale. For example:

1-: In To P. Rupert, published in The Character of a London-Diurnall: With several select Poems ([London?]: [s.n.], 1647), by the English poet John Cleveland (1613-1658):

The terrour of whose name can out of seven,
(Like Falstaffe’s Buckram men) make flye eleven.

2-: In Some Remarks on the Minute Philosopher. In a Letter from a Country Clergyman to his Friend in London (London: Printed for J. Roberts, 1732), by the English memoirist and political writer John Hervey (1696-1743), 2^nd Baron Hervey—interestingly, Falstaff’s eleven men in buckram have become sixteen:

Since the Minute Philosopher pretends his Book is written with an Intention only to administer an Antidote to the Poison of Free-thinking, to give a Solution to the Doubts of modern Scepticks, and stop the Apostacy of the present Times; why does he immediately, in his first Dialogue, by a quick Gradation, (not to be paralell’d by any thing but Sir John Falstaff’s Account of his sixteen Men in Buckram) work up his Free-thinkers into avow’d, confirm’d Atheists?

3-: In Essay XIII. Of Avarice, published in Essays, Moral and Political (Edinburgh: Printed by R. Fleming and A. Alison, for A. Kincaid, 1741), by the Scottish philosopher David Hume (1711-1776):

We find in common Life, That when a Man once allows himself to depart from Truth in his Narrations, he never can keep within the Bounds of Probability; but adds still some new Circumstance to render his Stories more marvellous, and satisfy his Imagination. Two Men in Buckram Suits became eleven to Sir John Falstaff before the End of his Story.

The earliest occurrences of the phrase men in buckram that I have found are:

1-: With explicit reference to Falstaff’s tale, from A Letter from a Freeman of the City of Chester, to his Friend in London; Containing a True State of the Merits of the late Elections there: With Observations upon the Free Briton Extraordinary of the 12^th of March 1732 (London: [s.n.], 1733):

Sir, the Letter-writer in the Craftsman suggested somewhat further than the Free Briton hath thought fit to mention: He said, that Mr. Manley’s Friends well knew from their Proceedings with the Mayor, and from the Constitution of the City, that it was not intended that any Persons should be made free the Night that the Pentice was demolished; for that nothing of that Kind could be done without calling an Assembly, and that no Summons’s were sent out for that Purpose: Hath the Free Briton attempted to give an Answer to this Fact? No, Sir, it was not to be denied, and therefore he is under the Necessity of supposing a Case that never was, nor was intended: That an Assembly was called, and 300 Honorary Freemen were to be made, and then, like Sir John Falstaffe, he puts the Negative upon the Proceeding, and with his Myrmidons knocks these Men in Buckram down.

2-: From Some Further Particulars in Relation to the Case of Admiral Byng. From Original Papers, &c. By a Gentleman of Oxford (London: Printed for J. Lacy, 1756):

The bare Hint of an Escape, though started only by themselves, and never so much as dreamt of by the Prisoner, was now to be countenanced, by new Precautions, such as additional Bolts and Bars, additional Guards of Soldiers, and as if all were not sufficient, a Boatswain and twelve Men of the Hospital by way of Supplement, to watch in the Court below.
Nor was it long before this new Officer was made, to see four Men at his Window in the Middle of the Night; upon which the Alarm was given, strict Search was made, the Officer upon Duty leading the Way,—and though these Men in Buckram were not to be found, nor any Trace that they had ever been there (the Marshal himself sleeping in the outer Room, and his Prisoner in the Inner,) yet this Figment was also to have an Air of Truth thrown upon it, by a further Parade of new Fortifications.

3-: From a letter published in The Leeds Intelligencer (Leeds, Yorkshire, England) of Tuesday 15^th May 1770—writing from Chelsea Hospital, the author, “a poor maimed Pensioner”, ironically adds in buckram, I suppose to 40,000 men:
—Context: In March 1770, British soldiers, under the command of Thomas Preston, had shot and killed several people while being harassed by a mob in Boston, Massachusetts:

All the news-papers are now full of the unhappy disturbances at Boston. There are different accounts; God knows how it is, my brother soldiers may have been to blame, but I hope they will not be condemned without an impartial hearing; and I am sure our gracious Sovereign is too just to suffer Capt. Preston, and his unfortunate companions, to fall victims to rancour and malice. How cruel is the alternative that a poor soldier has on these occasions; to be knocked in the head, or by resistance, expose himself to an ignominious death! however much I felt on this occasion, I could not help smiling at their beacon, and their tar-barrel, that is seen 80 miles; and their 40,000 men (in buckram, I suppose,) to be assembled in 40 hours!

4-: From the news from London, published in The New-York Journal; Or, The General Advertiser (New York City, New York) of Thursday 30^th December 1773:

Mr. O’Kelly, the Irish candidate, for Worcester, has, as the friends tell us, no less than four hundred voters out of two hundred and thirty freemen resident in London. His men in buckram at Worcester, are so numerous, that it is generally thought he will not stand a pole.