"I do not know exactly myself."
Translation:Ich weiß es selbst nicht genau.
They may both be correct translations for the word know, but they aren't synonyms and can't be used interchangeably. "Wissen" means "to know (about/how to do) something", while "kennen" is "to know somebody". Give this a read for more information http://german.about.com/library/anfang/blanfang16.htm
I don't know about every level, but "myself" is very commonly misused in English, and the positioning of exactly is important, so you may have misunderstood the meaning. I take it to mean either "I do not know the exact X (quantity/details/etc) either." (in reply to "I don't know the exact X; what are they/is it?") or "I don't personally know the exact X. [However, they are available…/However, this person does… etc]". „Kennen“, AFAIK, refers to being familiar with something or someone (while „wissen“ refers to understanding or being aware of something, usually a piece of information), so I don't think it would work here (how can one be "exactly familiar"?). Also, you don't seem have anything indicating "myself".