Especially used in (as) flash as a rat with a gold tooth, the phrase a rat with a gold tooth designates a person—usually a man—who, in spite of a superficial smartness, is untrustworthy.

In this phrase, the noun rat refers to a deceitful or disloyal man. The image is that, despite the gold tooth, a rat’s basic nature cannot change.

For example, Bill Deane used the phrase in the review of Vintage Pierpont (Sydney: Allen & Unwin, 1985), by Trevor Sykes—review published in The Canberra Times (Canberra, Australian Capital Territory) of Saturday 15^th March 1986:

To Pierpont, cynicism and scepticism are indispensable for survival in the corporate financial jungle. […] He continues to refuse to suspend his disbelief at company annual reports and audit statements, accountants being regarded with only marginally less distrust than might be accorded a rat with a gold tooth.

These are, in chronological order, the earliest occurrences of the phrase a rat with a gold tooth that I have found:

1-: From the review of The Long-distance Search for the Great Australian Funnybone, a television programme broadcast on ABV-2 on Tuesday 18^th July 1972—review by John Pinkney, published in The Age (Melbourne, Victoria) of Friday 21^st July 1972:

The programme, which promised to define the antipodean sense of drollery, but wisely chickened out, was, largely, a delightful anthology of rural pub persiflage.
From singleted soil-tillers—so earthy they might have been uprooted from a nearby paddock—came country tales and sayings which had about them the smell of centuries.
For example, one drinker’s definition of a drover’s breakfast (“A leak and a look around”) was used—and credited as a hoary saw—by Lawson, in a story for the old Bulletin.
But old or recently minted, there was a pungency about the lines the drinkers delivered—their camera-nerves deadened by soothing lager.
“Dressed in this suit,” said one unaccustomedly sartorial laborer, “I feel I’m bungin’ on more side than a rat with a gold tooth.”

2-: From Ginger Meggs comes home, by the Australian television journalist Bill Peach (1935-2013), published in The Sun-Herald (Sydney, New South Wales) of Sunday 27^th August 1978—Bill Peach told the story of Ginger Meggs, “Australia’s most enduring comic strip hero”:

There are two […] characters whose aim in life is to prevent Ginger having fun. One is Eddie Coogan, his arch rival for the affections of Min. Eddie is the ultimate lurk-man. He is always flush with money—money which one suspects the pestilential Coogan can only have acquired by foul means.
Eddie is as flash as a rat with a gold tooth. He patronises Ginger, heckles him, attempts at every turn to trip him up or do him down. And no trick is too filthy for the Coogan repertoire.

3-: From Clothes maketh the yachtsman, by Ron Saw, published in The Bulletin (Sydney, New South Wales) of Tuesday 31^st October 1978:

“Are we,” asked the for’ard hand, “entertaining royalty aboard, or something?”
“No.”
“Are we going ashore to a garden party, or perhaps a levee, at Government House?”
“No.”
“Then would you mind telling me why you’re all dressed up like a pox-doctor’s clerk?”
I looked down at my clothing. I was wearing clean white shorts, white socks and blue deck-shoes, and a red shirt; not, I’d have said, an overstated ensemble; certainly not one to bear comparison with a pox-doctor’s clerk.
As far as I know I’ve never seen a pox-doctor’s clerk, but whenever I’ve thought about one, I’ve seen some sneak wearing a mauve suit and a tie-bar, with a stone in it, just below the knot of his tie, and probably a lot of Californian Poppy glazing the tops of his ears. Flash as a rat with a gold tooth.

4-: From The Australian slanguage: A look at what we say and how we say it (North Ryde, N.S.W.: Cassell Australia Limited, 1980), by Bill Hornadge (1918-2013):

Flash as a rat with a gold tooth.

5-: From Dubious value of our cultural landscape, by Maurice Dunlevy, published in The Canberra Times (Canberra, Australian Capital Territory) of Saturday 28^th March 1981—here, the phrase is applied to two localities:

After I had read the arguments by Jeans and Spearritt last week that we should treat the cultural landscapes of New South Wales as an open air museum I set off last Saturday to test them.
In ‘The Open Air Museum’ (Allen and Unwin, 154pp., $18.95) D. N. Jeans and P. Spearritt argue that the evidence of our history lies not only in dusty tomes but in our landscapes.
[…]
Jeans and Spearritt argue it is time to put away aesthetic considerations and concentrate on cultural significance. It sounds fine in their book but I found it not nearly so impressive when surrounded by traffic lights, a colony of garden gnomes and the Winchcombe and Carson sheds.
Nor was the crass commercialism of Berrima very impressive. If the price of preservation must be the sale of knick-knacks to Sydney trendies, perhaps it is too high a price to pay. Berrima used to be a sleepy 19^th-century village that survived into the 20^th century, just as the Rocks used to be a delightfully grotty survival of the convict era. Now they’re both as flash as a rat with a gold tooth.