The phrase "a flimsy sheet of" is correct and usable in written English.
It can be used to describe a thin, weak, or insubstantial piece of material, often paper or similar substances.
Example: "He handed me a flimsy sheet of paper that barely held together."
Alternatives: "a thin layer of" or "a delicate piece of".
Back they went with Ms. Pressman, who checked for drafts by holding a flimsy sheet of paper and a lighter to all the windows.
As a party trick, he can tear up a pack of cards as if they are a flimsy sheet of paper.
Neighborliness: It is good manners to shelter unfortunate fellow pedestrians, covering their heads with a flimsy sheet of newspaper in vain attempt to ward off a spot of "wintry mix".
Gould wrote: "The data on the certificate is confusing and does not correlate with the known facts, but in the absence of evidence to the contrary, that flimsy sheet of paper is the only documentary proof that the SADF's foray into the narcotics industry ended in the stormy seas off Cape Agulhas".
On the third floor of an innocuous office building in southwest London, flimsy sheets of tracing paper are taped to the windows, leaving only an inch gap to glimpse the real world outside.
The family, four adult sisters and their five children, sought shelter from the sudden torrential downpour under a squat mesquite tree – and it was there, as they covered their heads with flimsy sheets of plastic, that they were struck by lightning.
They live in improvised tents, sleeping beneath flimsy sheets of plastic that magnify the heat and welcome the rain.
Flimsy sheets of paper decorated with the pale green faces of old men; little plastic squares the size and weight of business cards.
Deco-like lamps are made of flimsy sheet metal.
That wall paneling didn't stop the wind from seeping through the flimsy sheet rock.
In an interview on BBC radio last December, Clwyd wept as she described her husband's last hours, shivering under flimsy sheets, with an ill-fitting oxygen mask cutting into his face, wedged up against the bars of the hospital bed.
