It turns out that Kindle Previewer requires Java version 1.6, and Yosemite is on version 1.8. The fix is pretty simple.
Step 1 :: Download Java for OS X 2015-001. Close all of your Java applications (I just closed everything), and install it.
Step 2 :: Using the command-line, open up /Applications/Kindle Previewer.app/Contents/MacOS/Launcher with vi or something similar. You can do this via the GUI as well. Right-click Kindle Preview.app -> Show Package Contents and drill down until you see Launcher. Open Launcher with some sort of text editing tool.
Step 3 :: Add the following line right below “#!/bin/sh”
I’ve seen some folks recommending the below line instead. But that’s not where Apple installed the Java 1.6 JDK on my Yosemite machine, so I’m not sure where that instruction came from, but your machine might have it installed there.
Step 4 :: Open Kindle Preview and it should be rocking now.