It is grammatically correct, but sounds too formal. I would not say that in a conversation... maybe if you were writing a book or something.

You are correct that "inclined to" usually refers to tendencies (example: "he's inclined to getting angry in situations like this") but it can also be used to express a preference when faced with a particular decision. Example: Do you want to eat at home tonight? No, I'm inclined to eat out.