The phrase couldn’t lead a flock of homing pigeons means is, or are, or am, incapable of organising the simplest event, task, etc.
—Synonyms:
– to be unable to run a whelk stall;
– couldn’t organise a piss-up in a brewery.

The phrase couldn’t lead a flock of homing pigeons occurs, for example, in a letter by one Gene Ertle, Jr., of Manasquan, published in The Coast Star (Manasquan, New Jersey, USA) of Thursday 5^th November 2009:

The past portrays the future and cannot be disregarded. It is not the probability of the re-occurrence of the abject failure of yet another federal program, but it is the certainty of failure as derived from the vast available data. On the record, the exalted ones inside the ethics-free Beltway zone couldn’t lead a flock of homing pigeons.

The phrase couldn’t lead a flock of homing pigeons originated in Australian politics ¹ in 1945, as a comment on Robert Gordon Menzies ². This comment is generally ascribed to the Australian politician William Morris Hughes (1862-1952).

¹ I will not, in this post, go into the ins and outs of the complex political events that gave rise to the phrase, to its misattributions and misdatings, as Australian politics really is a panier de crabes.
² The Australian politician Robert Gordon Menzies (1894-1978), who was elected as the first Leader of the Liberal Party of Australia in February 1945, was the Leader of the Opposition from September 1943 to December 1949.

However, the text containing the earliest occurrence of he couldn’t lead a flock of homing pigeons that I have found indicates that William Morris Hughes denied having coined this phrase; this text is It was red herring week in the back room, published in the Sunday Telegraph (Sydney, New South Wales) of Sunday 1^st July 1945—Robert Gordon Menzies was nicknamed Ming:

Someone recalled that at the height of his last fight with the Opposition Leader, Billy Hughes had said that Ming “Can’t lead and won’t follow.”
W.M.H. repudiated authorship of the newest anti-Menzies crack—much as it was enjoyed by friend and foe alike—“He couldn’t even lead a flock of homing pigeons.”

The text containing the second-earliest occurrence of he couldn’t lead a flock of homing pigeons that I have found attributes this phrase to an unnamed “member of the Opposition”; this text is Menzies—Leader: An Inglorious Record, published in The Westralian Worker (Perth, Western Australia) of Friday 10^th August 1945:

Eventually Mr. Menzies regained the leadership but as one member of the Opposition said, “he could not lead a flock of homing pigeons.”

The phrase he couldn’t lead a flock of homing pigeons then occurs in Notes From The National Capital, a correspondence from Canberra, Australian Capital Territory, published in The Labor Call (Melbourne, Victoria) of Thursday 6^th September 1945:

Fadden ³ takes a secret delight in the comment still going the rounds since early in the session: “Poor old Bob—he could not lead a flock of homing pigeons.”

³ This refers to the Australian politician Arthur Fadden (1894-1973).

In the following from the Labor Call (Melbourne, Victoria) of Friday 8^th April 1949, not only is the phrase couldn’t lead a flock of homing pigeons ascribed to William Morris Hughes, but it is also misdated:

A LIBERAL SPEAKS ON THE LIBERALS
HOW FRANK BROWNE APPRAISES BOB MENZIES

Every week, a Sydney public relations consultant named Prank Browne, who has contested Federal and State parliamentary seats in New South Wales on behalf of the Liberal Party, circulates “for the confidential information of subscribers” a news digest entitled “THINGS I HEAR.” […] Some good friend has given “Labor Call” a copy of the February 28 issue of “Things I Hear,” in which Mr. Browne speaks without inhibition on the subject of Mr. R. G. Menzies and his fitness to lead the Liberal Party. […]
Under the heading, “CAN’T WIN WITH BOB,” Mr. Browne has this to say about the Leader, whose banner he himself has carried:—
[…]
“In regard to the […] charge […] of incapacity, there is aboundant [sic] proof. He became Prime Minister on April 26, 1939. He inherited a large working majority. He failed to win a by-election as Prime Minister. In September, 1940, as a war-time Prime Minister, he went to the polls, and despite the fact that leaders under such circumstances have an almost unfair political advantage, he succeeded in losing it. Billy Hughes commented . . . he couldn’t lead a flock of homing pigeons.”

In the course of time, various dates have been assigned to the phrase couldn’t lead a flock of homing pigeons, and other persons than William Morris Hughes have been credited for its coinage. For example, the following is from a letter by one M. B. Orken, about Papua New Guinea’s political leaders, published in The Bulletin (Sydney, New south Wales) of Saturday 27^th July 1974:

Not one “leader”, not even, with great respect, Michael Somare ⁴ himself, makes any national appeal outside his own particular district or in most cases outside his own particular extended family or clan grouping. And, with few exceptions, even in this limited field, when it is a matter of conflicting personal self interest, then none of them, to use the late Artie Fadden’s picturesque phrase, “could lead a flock of homing pigeons”.

⁴ Michael Thomas Somare (1936-2021) became the first Prime Minister of Papua New Guinea in September 1975.

—Cf. also another Australian political phrase: boudoir bandicoot.