This is a recipe that only the Food52 test kitchen can answer. A cup of flour is usually, depending on the author, equivalent to about 125 grams, although the side of the bag of flour typically says it's 120. In reviewing recipes from the Food52 editors that provide both mass (grams) and volume measures, the Food52 cup of flour can range from 120 to 146 grams per cup.
Given that wide swing of possible conversions, and the relative importance of the flour in this recipe, you really need to find out the actual volume amount used by the test kitchen.
You could also post a comment to the recipe, asking those who have made the cookies if they converted to volume and if so, what worked (or didn't).
Almond flour tends to be a bit more predictable, but you might as well let the Food52 editors weigh in on that, too.
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Given that wide swing of possible conversions, and the relative importance of the flour in this recipe, you really need to find out the actual volume amount used by the test kitchen.
You could also post a comment to the recipe, asking those who have made the cookies if they converted to volume and if so, what worked (or didn't).
Almond flour tends to be a bit more predictable, but you might as well let the Food52 editors weigh in on that, too.
Good luck! ;o)