According to a May 19, 2011 press release (Amazon Media Room:News Release) the Kindle for PlayBook app is coming soon:
Better late than never.All Kindle Books let you "Buy Once, Read Everywhere" - on all generation Kindles, as well as on the largest number of devices and platforms, including iPad, iPod touch, iPhone, Mac, PC, BlackBerry, Windows Phone, Android-based devices, and soon HP TouchPads and BlackBerry PlayBooks.