I cannot trace the origin of the phrase "in the blink of an eye," neither the earliest printed record of the expression.
Surprisingly, even the Google Ngram Viewer returns a "NO" result. How come?
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It is recorded by Robert Manning of Brunne, in Handlyng synne, 1303: "Yn twynkelyng of an ye"
It is also used in the Bible, 1 Corinthians 15:52 (King James Version): In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
It was later used by Shakespeare in The Merchant Of Venice, 1596: "I'll take my leave of the Jew in the twink of an eye”
An early usage example is from Chambers's Edinburgh journal of Popular Literature conducted by W. Chambers, 1874:
She 's that quick, she was gone like the blink of an eye ; and, besides, Jenny, she is not one to be easily hindered when she 's set upon a thing.
And from A Cook Book, 1876:
Ho ! all ye poor sinners , in search of good dinners , You'll surely be winners , if our plan you will try ; Only just take a look in this wise little book , And ' twill teach you to cook in the blink of an eye.