What's the exact error message you're getting? Is there something I need to do in order to successfully run 1.23.1 (or 1.17!) on this Mac?. Downloaded 1.23.1 from the link given at the pinned post at the top of this thread.
I couldn't run Kindle 1.17 for Mac on High Sierra (10.13, to which I just updated) - got the 'need to update file type' message (assume that means 64-bit files), and the app won't even launch.