You could try blocking access to the various domains Amazon uses to push updates, as explained
here. I cannot confirm whether this covers all domains for all Amazon markets; for this reason I’m personally a bit wary to try it, but it is the simplest if you want to keep your device online.
Besides leaving your device in flight mode, another foolproof method is to fill your device with data so that only a few dozens megabytes are left, i.e. too small to store any update file. I had some success with
this method, but in the end I gave up due to frequent and annoying reminders that my device is full, and also because restarting the device did delete all the files; but your mileage may vary.