I've seen some threads about this topic but, IIRC, the consensus was that stopping the Kindle for PC app from updating couldn't be done. I
think I found a way but, of course, wanted to post what I've done so others who are move technically proficient might advise the community.
After I installed v2.3.0, launched, and registered my account, my books sync'd as expected. The threads I read warned about a silent update being DL'd even though I unchecked the auto-update choice in the app's Options. Indeed, I found that update (v2.7.1) waiting in this folder:
C:\Users\Mac User\AppData\Local\Amazon\Kindle\updates
(Mac User is my home folder - I'm now a Windows user but old habits die hard.

)
I trashed that updater app, then I changed the permissions of that "updates" folder by disabling inheritance in the Advanced section (converting to explicit permissions), then removing the System and Admin users and, finally, changing my Mac User permissions to "read" only. I've attached a png showing the final appearance of that dialog.
If I'm right, I've essentially locked that folder from being changed so Amazon can't download the updater. I did have the Kindle app running this whole time (so Amazon wouldn't attempt another sneaky download upon the next launch). Now, with the changes to that folder complete, I quit the Kindle app. When I launched it again, I got a dialog asking me if I wanted to update to v2.7.1 which I declined with the "skip for now" choice. (I expect Amazon will push that update again eventually.) I quit and launched the app a number of times since then and that "updates" folder remains empty.
Perhaps I found a solution? Even a stopped watch is right twice a day.