I measure by weight, but sometime I get a recipe in cups for flour.
What density (oz / cup) should I use?
The answer depends on the type of flour, and sometimes even the brand of flour, and how the flour is measured out. I personally use November's Mass-Volume Conversion Calculator at http://tools.foodsim.com/
for those flours in the pull-down menu, but if you look at the labeling information on a bag of King Arthur all-purpose flour or a bag of King Arthur bread flour, a cup of flour "weighs" 4.2 ounces (based on 76 1/4-cup servings in a 5-lb. bag). I assume that King Arthur based that number on using the method of flour measurement as described at their website at http://www.kingarthurflour.com/tips/bakers-dozen.html,
as follows: Because flour settles and compacts in storage, fluff it up before you measure. Then, gently sprinkle it into your measuring cup and scrape the excess off with the back of a knife. This will ensure a 4 ounce cup of flour rather than the 5 ounces you would have if you scooped it out with your cup.
I recently did several one-cup weighings of King Arthur all-purpose flour using the Textbook method of flour measurement defined at Reply 21 at http://www.pizzamaking.com/forum/index.php/topic,6576.msg56397/topicseen.html#msg56397,
and got 124.8 grams per cup, or 4.4 ounces per cup. When I previously did similar weighings for the King Arthur bread flour, I got 4.56 ounces per cup.