I don't mean to pick on you, specifically, because you're far from the only person who's made such a comment, but I sure do get tired of hearing people describe the FairTax as "inflationary" on a conservative web site.
Same.
It is purely inflationary of itself regarding any contracts that tie wages or purchases to any price index. Wage agreements, I should think, would be more directly affected, but we would have to see how exactly this would play out. (C'mon mate, that should go w/o saying.)
Of course, if enough people get sick of a 'fair' tax regime, it might become somewhat deflationary, as people go outside the regime and are forced to discount prices as a condition of doing business and not getting caught.