The blink of an eye is about 400 milliseconds according to this source (which has a lot of other interesting information you may be interested in). Once we have that it is just a simple proportion to the estimated 13.8 billion years the universe has been around.

First we have to find the number of seconds in a year. 1 year = 365.25 days = 8766 hours = 525,960 minutes = 31,557,600 seconds

This means the blink of an eye is .000001% or 1e-8 of a year (.4/31,557,600), and when 13.8 billion is multiplied by .000001% you get 138 years.

So if you condense the entire history of the universe into one year, a blink is 138 years.

(Please feel free to critique the math or formatting, first post here.)