Curmudgeon10-
Your Roku 3s were extremely capable at the time of their release in 2013, but they may be reaching the point where they are underpowered and slow for running some of today's bloated apps. Roku 3s have 512 MB of memory, while today's offerings have faster processors and (with the exception of the bottom end non-4K Express) have 2 to 4 times the memory.
The nature of streaming apps is that their developers keep updating and adding code to their apps which causes them to use up more of the capabilities of the devices they are being streamed on. It's possible a recent update to the Prime app has pushed it over the edge for your Rokus. I can find no listing on the Amazon website of which Roku models they currently support.
You might possibly find Prime runs better if it is the first app you run after rebooting the Roku 3 so that you are starting with a clear memory cache.