In a blink of an eye or in the blink of an eye

The phrase, “in the blink of an eye,” is an idiom in the English language that has a somewhat literal meaning; the phrased is used for when a very short period of time passes. Speakers and writers use “in the blink of an eye” to refer to anything that seems to have happened quickly. In actuality, though, English speakers often use this phrase to apply to things that happened over a long period of time, but which appeared to happen quickly in retrospect.

It’s easy to see how this saying relates to a very quick time frame. The fact is that it takes only a fraction of a second for someone to blink his or her eyes. A common synonym would be "instantly."

In a blink of an eye or in the blink of an eye
The phrase "in the blink of an eye" refers to something that happened quickly.

Another idiomatic phrase that is used in place of “in the blink of an eye” is a bit more colorful. English speakers often use the phrase “in two shakes of a lamb’s tail” in place of the more literal reference. Here, listeners assume that it does not take a lamb very long to shake its tail.

Other synonyms consist of single words. For example, someone who might be talking about a very short period of time might say “in a jiffy” or “in a nanosecond.” The phrase “coming right up” is used in similar situations where someone is waiting for something.

It’s important to note that the phrase, “in the blink of an eye,” is rarely used to communicate to someone who is waiting for something. In contrast to some of the above phrases, this phrase is more commonly used in reflection, nostalgia, or in a similar situation to express a feeling about how quickly something has happened. For example, “the kids grew up in the blink of an eye” is a very common application of this phrase. The children in question have in fact taken years to grow up, but the speaker is using the idiom to indicate how quickly the long period of time seemed to pass. This sort of use demonstrates how English speakers and writers most often use “in the blink of an eye” as a fancier way to say that they have perceived time to have passed quickly.

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In the blink of an eye is a very short time in its literal sense. There is no need to use "like" here— it isn't like an instant, it is an instant.

Time flies is an idiom which evokes the general sense that it moves quickly, and more quickly than we perceive it, but not necessarily in an instant. The old saying is Time flies when you're having fun, meaning time seems to pass more quickly when having fun, but not that the fun is over with as soon as it started.

They are both clichés, and I would try to think of better expressions perhaps more directly related to the topic. If you do use one, remove the other, as they are redundant. You could say, for example,

From Longman Dictionary of Contemporary Englishin the blink of an eyein the blink of an eyeFAST/QUICKvery quickly → blinkExamples from the Corpusin the blink of an eye• A full volley will rip through the toughest regiment causing immense casualties in the blink of an eye.• I had read somewhere that all the greatest discoveries had been made in the blink of an eye.• He went from frozen stillness to liquid and menacing movement in the blink of an eye.• It was the uncertainty, the thought that all my happiness could be smashed in the blink of an eye.• He would be up and after them in the blink of an eye.• How often does it lose a week's work in the blink of an eye?

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In a blink of an eye or in the blink of an eye
In a blink of an eye or in the blink of an eye

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So quickly as to seem almost imperceptible (i.e., in the space of time it takes a person to blink). The high-speed camera reveals how the frog uses its specialized tongue to capture the insect in the blink of an eye. Working on Wall Street, you get used to massive financial changes happening in the blink of an eye.

Farlex Dictionary of Idioms. © 2022 Farlex, Inc, all rights reserved.

So quickly as to seem almost imperceptible (i.e., in the space of time it takes a person to blink). The high-speed camera reveals how the frog uses its specialized tongue to capture the insect in the blink of an eye. Working on Wall Street, you get used to massive financial changes happening in the blink of an eye.

Farlex Dictionary of Idioms. © 2022 Farlex, Inc, all rights reserved.

extremely quickly: In the blink of an eye, he was gone.
"In the blink of an eye" is a bit of a hyperbolic metaphor, and a bit of a tired cliche. I'd recommend avoiding both of those effect and using something prosaic, literal, and fairly natural: "in a single moment".
Noun. (idiomatic) A moment (a very short period of time).
1. To close and open one or both of the eyes rapidly. 2. To look in astonishment or disbelief, typically with the eyes blinking: stood blinking at the money they found in the drawer; blinked at the results of the experiment. 3.