I did a quick search for him on the Washington state digital archives site here: http://www.digitalarchives.wa.gov/Home
but I did not see a Frank Norris that appeared to be him. You may want to do a more thorough look at the data on that site.
I also recommend you look at the cemetery transcriptions on this site:http://mrail.net/wash/spokane.htm
Should you find he died in Spokane, and have a death date but still don't know where he is buried, then you may be able to find an obit for him in the Google News Archive of the Spokane papers here:http://news.google.com/newspapers/