Actually, looking at the listing again, and searching for the word "kosher," it turns out that:
"All of our coffees are certified Kosher by a local San Francisco area rabbi from the Orthodox Rabbinical Council of San Francisco. Some of our coffees are Star K certified."
So it probably DOES vary by flavor.
And in case you were hoping, I took a quick look at the company's website and didn't find any flavored ones with a Star-K.