Cake, Bread or AP? My goal is a 'chewy', 'moist' brownie. I have always used AP in the past, but am wondering if an alternative flour might improve the final result.
Short and sweet... Use cake / pastry flour. At 5-7 % protein vs. 11% for AP vs. 13% + for bread flour, that means a lot less gluten formation. This protein, when mixed with water and subjected to mechanical working is what produces gluten. The higher the protein percentage, the 'tougher' (due to the gluten) the final product. Always use cake or pastry flour when making any type of cake, even brownies. And a little extra egg won't hurt, either.
DO NOT use cake flour--use all purpose. The lower percentage of protein in cake flour makes a "chalkier/crumbly" texture. If you're going for chewy/fudgy brownies, all purpose is the way to go! I actually made a batch today using cake flour, and was so angry at the result. I made a new batch using AP flour (to redeem myself), and it turned out wonderful!
I think the type flour used will have less of an effect than the amount, especially if your recipe uses lots of chocolate, butter, and eggs. My go-to Brownie recipe uses all-purpose flour (relatively little compared to the rest of the ingredients), and the brownies come out chewy and moist every time.