I went to a talk yesterday at the Johnson Society of London given by Jock Murray, Emeritus Professor of Medical Humanities at Dalhousie University, Canada. He was speaking about Samuel Johnson's well-documented eye problems and his talk was entitled Blinking Sam: What Caused Johnson's Poor Eyesight?
Johnson's friend Sir Joshua Reynolds painted four portraits of him and one of them is known as the Blinking Sam portrait, as it shows Johnson with a book very close to his face (see here). It was Johnson himself who came up with the epithet; on seeing the portrait he is said to have complained that he did not want to "be known by posterity for his defects only". When it was pointed out to him that Reynolds did not mean any harm, and that he had shown himself cupping his ear in his self-portrait, thus drawing attention to his deafness, Johnson is said to have remarked "He may paint himself as deaf if he chooses, but I will not be Blinking Sam".
In the 20th century 'blinking' began to be used as a mild expletive, and you will still hear some people (usually older people) saying things like "blinking idiot" or "blinking nuisance". Such phrases are usually said by people who would never dream of swearing, and 'blinking' replaces the stronger 'bloody'. There are other similar 'bloody' substitutes eg blooming, blasted and blankety.
In Shakespeare's The Merchant of Venice, Portia's second suitor, the Prince of Arragon, says on opening the silver casket "What's here? the portrait of a blinking idiot". Here, the word 'blinking' is probably literal -- it perhaps refers to the fact that the picture inside the casket shows the jester squinting. Johnson uses the above quotation to illustrate his definition of blink ("to see obscurely") in his famous dictionary. The headword 'blinkard' is also in Johnson's Dictionary with the meanings 1) One that has bad eyes and 2) Something twinkling. The OED has another sense for 'blinkard' and one that goes back to the 16th century, namely "one who lacks intellectual perception", which explains perhaps why Shakespeare attached the word 'blinking' to 'idiot'.
There's much more about Johnson's eyesight problems in this article.