The books should come around release, or a little after. I know that for the last 3 pre-releases I've ordered that the products (including KoTS) shipped earlier than they said it would AND the items got to me all on the release day, and this is with Standard shipping. Free shipping does, actually, add some days to this, in my experience, but standard hasn't. The posted date for me to receive the items was always several days after release but if you follow the Tracking button you can see the items get to you much quicker, and I've never had to wait until the actual predicted date posted on the site. At least with pre-releases.
I expect to get my books on the 6th from Amazon and no later than the 8th. If Tracking doesn't show the books as being in Phoenix come the day before release than I will go buy a PHB from the local hobby shop to read and keep as an extra.