The Australian rhyming phrase one flash and you’re ash is a slogan used by opponents of nuclear weapons—cf. also ‘better red than dead’ – ‘better dead than red’.

The earliest occurrence of one flash and you’re ash that I have found is from The Sunday Mail (Brisbane, Queensland) of Sunday 3^rd May 1953:

Reds’ slogans ready for march counter
Big police turn-out to keep order for march

Police reinforcements will make sure that to-morrow’s May Day march in Brisbane will be orderly.
Official Labour organisers have been granted a permit for the march, but the Communist-controlled Trades Hall Council has been organising militant unions.
In Room 9 of the Communist-dominated Trades Hall are stacks of Communist propaganda. […]
[…]
One of the placards in Room 9 says “Ban the A-Bomb—One Flash and You’re Ash.”
Another states that Hitler began by banning Communists.

The second-earliest occurrences of the phrase that I have found are from the Tribune (Sydney, New South Wales) of Wednesday 5^th May 1954:

– from this advertisement:

ONE FLASH—AND YOU’RE ASH
RADIO-ACTIVE fish circle the world.
Menzies ¹ backs further H-Bomb tests.
Help to oust this war crazy government on May 29 ² by selling more copies of the pamphlet “THE H-BOMB, JAPANESE REARMAMENT AND YOU.”
6d. from Current Book Distributors.

– from the account of the May Day march in Sydney:

May Day marchers said . . .
Ban the H-bomb and lift wages
Most prominent demands in Sunday’s record May Day march were for a ban on the H-bomb, for increased wages and margins, and for the ousting of the Menzies Government ¹ on May 29 ².
[…]
Slogans that won applause included: “Support the Empire Games Appeal . . . Be peace-active, not radio-active . . . H-bomb cremates all men equal . . . Hands off Indo-China . . . Unity for Peace . . . Reduced prices for essential foods . . . H-Bomb—One flash and you’re ash . . . Petrov-y ³ Menzies on May 29.”

¹ Robert Menzies (1894-1978) was Prime Minister of Australia from 1939 to 1941 and from 1949 to 1966.
² The 1954 Australian federal election was held on 29^th May.
³ Vladimir Petrov (1907-1991), Third Secretary of the Soviet embassy in Canberra, defected to Australia in April 1954.

The phrase is also used in New Zealand. For example, the following is from U.S. ship ignites Zealand strike, published in the Chicago Daily News (Chicago, Illinois) of Friday 27^th August 1976:

Wellington, New Zealand (UPI)—Arrival of the American nuclear-powered cruiser Truxton Friday touched off a strike by dock unions, stranding thousands of passengers and disrupting ferry service between New Zealand north and south islands.
[…]
Sailors from the Truxton went ashore on liberty, accompanied by whistles and jeers from about 80 demonstrators who waved banners reading, “Be active, not radioactive,” “One flash and you’re ash,” “Remember Hiroshima” and “Keep New Zealand nuclear free.”