I suppose you could call it a mistake, or at least a mistaken understanding of what the word "inclination" actually means. However as this man uses a double negative in one of his statements:
I don't have no inclination of where she is
we already know he is from a a particular class of English speakers who are, let's say, not especially "formal" with their grammar. I would conclude that he's either accustomed to misusing "inclination", or he learned it from the people he associates with.
However we shouldn't discount the possibility that the meaning of "inclination" has changed from the standard dictionary definition, and become "fuzzy" as various people use it in a different way. Many words have been changed through colloquial use -- for example, as weird as it may sound, the word "literally" often is used to mean "figuratively".
I, personally, would never use "inclination" in this way. I would either say:
I have no idea where she is.
I'm not inclined to tell you where she is.
I suspect if this person used "inclination" this way in something like a court of law, he would be asked to clarify his statement.
[Edit] Per Tᴚoɯɐuo's answer: it seems that "inclination" has an established use as a colloquialism or dialect. It's not one I am comfortable with, personally, but it may be fine in this person's conversational circles.
As Tᴚoɯɐuo says, a paraphrase of this particular use might be something like:
I don't know enough (or pretend to know enough) to be able to lean in any specific direction that points to where she is.