Did you go online to "Manage Your Kindle" and have the book resent to your Kindle? Occasionally, I will purchase a Kindle book and it doesn't show up on my Kindle. If I go and have it resent it usually shows up within a minute.
Do you have Whispernet turned on? If it's not on the book can't be downloaded.
Do you have decent coverage. Depending on your location Whispernet may not be relaible enough to download books. In that case, you can download the book to your computer and use the USB cable to transfer the book to your Kindle.
BTW, welcome to Mobileread!
