Google (now a billion dollars richer) offers 1210 web pages on which this word -- honestness -- appears .. so, for descriptivists, this is ample evidence that somebody is using it.
As it appears to be entirely synonymous with "honesty" there seems little reason for its existence. In all the stuff indexed by Bartleby.com, there is not one reference to this word.
I don't use it. I wouldn't use it ... except, perhaps to create a parallelism between it and another word ending the same way, e.g. earnestness and honestness.
