To obtain an obituary, one must look in every newspaper for the county, then hope to be lucky that one was posted for the area that he lived; or, that he even lived in the County. As Stevens County lies above Spokane County, his obituary could have been posted there...if there was family there to purchase it. Not all deaths had obituaries.
With that said, this site: "http://www.rootsweb.com/~wasteven/cemetery.htm" has cemetery transcriptions for Stevens County. While some of them haven't been transcribed. Highland / Calvary Cemetery has a Rose J. Kostka...no dates. I will let you go through the list.
The 1930 US Census did not show a Frank Kostka born around 1867.
If you have spouse, children, parents, any additional information on him, that would help in attempting to find where he might have lived. His information in the WA Death Index has no further information. So, perhaps, he could have only been passing through?