As long as you're cooking by weight, not volume, and the amount of flour is on the low side (here it's a half cup), you should be able to use whatever GF flour you have on hand. The eggs are doing most of the work here. The exception would be coconut flour...that stuff sucks up liquid like crazy. Be careful using it.
I have a homemade mix I do that's a combo of brown rice flour, white rice flour, arrowroot, and tapioca and it worked beautifully. But again, I always bake by weight, never by volume.
(I've been doing GF baking for over a decade. If you want some science, look into America's Test Kitchen or Gluten Free Girl...they give good tips for ratios of starchy flours to whole grain flours that should help!)
I am gluten free and just removed the flour. They are more like a flourless chocolate cake, but there's nothing wrong with that! I do like like brownies with a little more cake feeling. I believe I will try them with one of my gluten free flour mixes. Measure for Measure and Better Batter will probably work, as well as King Arthur Measure for Measure flour.
Brownies don't really take to single-flour swap-outs. I would do a pre-made gluten-free flour mix (Cup4Cup, Pamela's). Or, if you want to buy multiple flours/starches/gums, I'd do a combo of brown rice flour, potato starch, and a 1/2 tsp of xanthan gum. If you choose the mix-your-own flours method, you'll be better-served if you do it by weight rather than measure. That's why Cup4Cup or Pamela's mixes can be better options; most people don't have digital scales at home. Good luck!
If you are trying to substitute gluten-free flours for AP flour make sure to do it by weight rather than by volume. Different flours have very different weights and that makes a big difference in the final product. In my experience I have had the best results when using a mixture of starch (like rice flour or tapioca) and whole-grain gluten free flours (like amaranth, buckwheat or even nut meals) to sub for the AP flour rather than using a single flour. That being said there is not so much flour in the recipe so a straight substitution might be fine.
With this recipe, you can use the following with varying taste and textural results: Brown rice flour, almond flour, and Trader Joe's Gluten Free flour mix. I have made them all.
My favorite brownies are -- http://food52.com/recipes/12472-raspberry-brownies. They are gluten free and delicious. You could compare the two recipes if you want to use the AM recipe, and splice in a sub for the flour.
I think you can definitely sub alternative flours for all-purpose, but I would use a blend. Rice flour on its own can be grainy, leaving the final texture with something to be desired. But I have had great success using a combination of rice flour, tapioca starch, and corn or potato starch. The starches round out the texture and provide structural support (not that brownies need very much of that).
Often, when baking GF goods, extra eggs are helpful because they do what gluten usually does--give structure and bind things together. Brownies usually have lots of eggs, so this isn't as much of an issue here. In fact, I agree with ChefJune, above. Brownies are very adaptable as they don't need much structure and usually have relatively little flour to begin with, particularly fudgy brownies.
I was in a Gluten-free Baking workshop Alice also attended a week ago, and she mentioned subbing alternative flours in brownies. I had recently made my tnt brownie recipe with chestnut flour, and she opined that brownies were great candidates for alternative flour because of their forgiving nature. I'd think rice flour would also work. Give it a go and let us know how it works out.
Peter Reinhart, who led the workshop, uses a lot of pecan flour as sub. If you are not nut-sensitive, the flavor of the pecan flour is wonderful. It does take a bit of skill with the food processor to get the pecans to just the right consistency w/o making a paste, though.
I'm not sure about rice flour, but I noticed in the comments that one person successfully used coconut flour. The full comment from juliunruly reads, "I made these with coconut flour. Used four eggs instead of two, and had to increase the cooking time by about 10 minutes (our oven also runs a tiny bit cool). They turned out fabulous--and this is the first time I've ever baked with "alternative" flour, so I'm not just saying that because I'm used to it. They really are great!"
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I have a homemade mix I do that's a combo of brown rice flour, white rice flour, arrowroot, and tapioca and it worked beautifully. But again, I always bake by weight, never by volume.
(I've been doing GF baking for over a decade. If you want some science, look into America's Test Kitchen or Gluten Free Girl...they give good tips for ratios of starchy flours to whole grain flours that should help!)
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Often, when baking GF goods, extra eggs are helpful because they do what gluten usually does--give structure and bind things together. Brownies usually have lots of eggs, so this isn't as much of an issue here. In fact, I agree with ChefJune, above. Brownies are very adaptable as they don't need much structure and usually have relatively little flour to begin with, particularly fudgy brownies.
Peter Reinhart, who led the workshop, uses a lot of pecan flour as sub. If you are not nut-sensitive, the flavor of the pecan flour is wonderful. It does take a bit of skill with the food processor to get the pecans to just the right consistency w/o making a paste, though.