My sister joined CEA-HOW which is similar to FA and lost a ton of weight. But yes, you're right--the going totally off of flour and sugar seems a bit extreme, but at the same time, there's good research and reasoning behind it.
Have you looked into regular OA (Overeaters Anonymous)? It's philosophy is less stringent and focuses more on finding a balanced way of eating consistently--no binging or eating those "trigger foods" that make you more likely to binge.
I think part of the FA philosophy is that simple flour and sugar are detrimental to most humans' weight and health. And there is tons of research to back this up. I fully support removing or significantly reducing the amount of carb/sugar intake. Whether to make it part of an addiction support group....I'm not sure.
For my sister, a program that prohibits flour and sugar was what she needed. She doesn't work, so she had time to prepare all of her fruits and vegetables and proteins. And, she needed a LOT of structure/limitations.
I'd say look into OA and Greysheeters as well and then figure out what will work best for you.