I wasn’t sure what rain rot was but it wounded like scald, which many of the horses on a station I worked on in the Northern Territory got during the wet season. I googled it and it turns out its probably the same stuff. I never encountered it before I worked up there (and that was many years ago now), and it only happened in the wet season, the place is monsoonal. Our head stockman used to mix up a mixture of diesel and something, it might have been vegi oil (it was about 18 years ago now, I can't quite remember exactly what it was), and we'd spray that on their back and it seemed to clear it up eventually. But anyway, when I googled it to see if rain rot was scald, the website I found recommended the original Listerine mouthwash, the foul tasting golden coloured one. It said that scaled/rain rot is caused by a bacteria that gets into the horses skin. Apparently you should fill up a spray bottle with the mouthwash and do a combination of spray it on and brush off the loose clumps of hair with a brush. Here is the link to the site.
http://juliaeverheart.hubpages.com/hub/How-to-Treat-Rain-Rot-in-Horses