Amazon is offering American Sniper download for as little as $0.99 (SD version). You can pay a bit more and get the HD version for only $1.99! This is the lowest rental price I see for this anywhere (outside of a free Redbox rental code as available).
You an actually buy the rental right now and will have up to 30 days to watch it. Then, once you watch it for the first time, you can view it as many times as you would like to in a 48 hour window.
Remember that you do NOT need to own a Kindle to watch movies. You can stream them on to many devices, including iPads and more!