I don't get it. Why would being bumped to Buiness Class help with his medical condition. Do feet swell less in business class? If so, and your brother knows that - him buying a business class seat is in order. I can't think why NWA should be the one to do the work for him.
You may not mean it, but your post comes across as "how can I sucker NWA to benefit my brother because he's got a health problem?" If they do bump him, I'll be getting a doctors statement for my trans-ocean flights - I'm sure the reduced stress of business class will be therapeutic to my aching feet