First we need to know the proportion of the entire population that got vaccinated. In 2015/16 which is the most recent year for which numbers have been published 45.6% of Americans over the age of 6 months were vaccinated.
In an average year the flu vaccine reduces your risk of getting the flu by 50 to 70% although the 2017/2018 flu vaccine currently seems to be somewhat less effective.
In an average year about 7% of the population gets the flu. The 2016 estimate of the US population is 323 million which means that you could reasonably expect about 22.6 million cases of the flu in a season. But if the flu vaccine is 50 % effective, that means the vaccinated people are only half as likely to get the flu. This suggests that about 6.6 million of the 22.6 million flu cases has had a flu shot. If the vaccine were 70% effective then only about 3.1 million of the flu cases would have been vaccinated.
This means that about 14–29% of flu cases can be expected to have been vaccinated or conversely that 71–86% of flu cases can be expected to have been not vaccinated
Interestingly, 90% of people who die from the flu were not vaccinated, which suggests that the flu vaccine reduces your risk of death even if you get the flu. Which is the main point of getting the flu vaccine in the first place.