“Blinky” is milk (or, rarely, another food product) that is beginning to turn sour. “Blinky” is used in Texas and other states in the South and Midwest.
 
     
Language in Texas 2000
blinky: milk that is turning sour (Southernism).
 
American Varieties - Texan
Is Texan a Thing of the Past?
Is the beloved Texas accent disappearing? Nope,  y’all. According to Pamela Colloff, it’s hotter than a two-dollar pistol.  (The research cited in this essay was first published in 2003.)
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And while Carol knew many of the older country sayings—a skunk was a “pole-cat,” and milk that about to turn sour was “blinky”—her daughter frowned at such folksy expressions.
   
Lost Words From Our Past
While I was reading Robbye’s letter (above) I thought of two really great words I haven’t heard in ages; “blinky” and “clabbered”. For those of you that were raised with an ‘icebox’ as opposed to a ‘refrigerator’ you will recognize both of these words. “Blinky” is is an unpleasant taste to milk just a short time before it soured. Both are a result of storing milk at too warm a temperature. If the milk is ‘blinky’, you don’t throw it away. You can use in bread or other cooked food. Now “clabbered” is the other side of soured milk. After it has soured it begins to turn into a solid somewhat less than jello in texture. The taste is foul (I think) and one of the first items that goes straight away into the slop bucket.
   
(Dictionary of American Regional English)
blink v
Of milk: to turn sour.[From blink to exercise an evil influence, bewitch, henceto sour (souring of milk being formerly ascribed to witchcraft)]
1905 Dialect Notes 3.70 Blink...To turn sour. Used of milk only. “The miolk’s blinked.” “It was so warm that the milk blinked.”
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blink adj =blinky
1883 Amer. Philol. Assoc. Trans. 14.45, Blink milk: “milk somewhat soured.”
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blink n
1895 Dailect Notes 1.384, Blink: sour milk.
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blinky adj. [blink v.]
1a Of milk: beginning to go sour.
1902 Dialect Notes 2.229
1b Of things other than milk: sour. infreq
1895 Dialect Notes 1.370, Blinky: sour. “The vinegar is blinky.”
 
8 July 1887, New York Times, pg. 4:
This is the season of the year when the country boarder eats salty ham and drinks blinky milk and has narrow escapes from mad bulls and playful goats, and imagines that he is recuperating his wasted energies.—Cincinnati Herald.
 
30 March 1908, Washington Post, pg. 4:
“But, speaking of that old Chicago fellow’s buttermilk idea, did you ever drink any ‘blinky?’ That will do just as much good toward prolonging life as sour milk, because it is a kind of sour milk.”
 
12 July 1919, Indiana Farmer’s Guide, pg. 14:
It required a vast amount of water from the old well in hot weather to keep the milk cool in the old milk trough so that the cream could rise before it got too “blinky” to make good butter.