Different doctors have different formulations but I thought that "magic mouthwash" is not an over the counter mixture (OTC) but a prescription one, in which case you should ask your brother's doctor for a script. I personally hated it and found that it made me gag and choke despite trying three different formulas but the majority of posts here at OCF found it helpful.
The best thing you can do for your brother's oral hygiene is to make sure the hospital gets you a referral to a dentist or prothodontist who specializes in oral cancer care. I was lucky that my CCC radiation department plus my ENT both recommended the same prothodontist. Once the mouth heals up, getting flouride trays to use daily for life is very standard.
I have all my teeth going on three years after diagnosis and TX and the month I took off of any standard tooth brushing & mouth care after surgery had zero impact - my mouth was just a mess of sores and far too sensitive to anything except water and seltzer water.
Charm