The Main Salmon (launching at Corn Creek) in late August will be fine. I have done this a couple of times in early September and this is a great time to do the river. The flow will be on the low side but the crowds are down and the weather can be great (or not so great depending on the day). Rafts in the 14'-16' would be best but you could get an 18' down without any real difficulty unless it is loaded to the gills. The camps are great, many with large beaches.
You can check out pictures of the primary camps at (hopefully this link works)
Main Salmon
Enjoy your trip.