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Kitchen floor already in place?
Onelayer of felt will do the trick if its only 1/16. Not sure if I like that too much but will do i there's isn't any other way. There is no way you will get that absolutely flat. The lumber may swell up in the wet month and shrink in the dry. That itself will be as much as 1/16.
Run it up against the tile and allow 1/16" -1/8" for fill
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