A few weeks back Amazon released a firmware update for its Fire tablets that broke a key feature. The update accidentally made it difficult to impossible to install third-party apps.
Now Amazon has released a new version of Fire OS 5.6, and it seems to fix the bug. Update 184.108.40.206 can be downloaded from Amazon. There's no mention of the bug in the changelog, but user reports suggest that the problem has been fixed.
If you have a late model Fire tablet, you can install the update by going to the settings > device > systems update menu, and telling the tablet to check for an update.
As an alternative, you can also download the update from Amazon and install it yourself.
I cannot, though. While Amazon did release an update for 4th-gen Fire tablets, they did not release one for my model.
I am one of the lucky few that managed to duck the problem entirely. How about you?