Slowdowns happen for various reasons on your streaming devices, but the good news is that it often doesn't mean it's the end for them. In fact, there are a number of things you can do that get your device running as good as new, or at least close to it. One of those is clearing the cache, and it's a common fix for Fire TV devices. Other streamers don't have a dedicated way of doing this other than restarting the device. To be fair, that gets the job done, and is often a quick fix.
The same idea applies for Fire TV devices, but it requires actually going through the process of clearing the cache. This works on all Fire TV devices, including an actual Fire TV. If you're running into slowdowns, try clearing the cache on your Fire TV device before you do anything. In my experience, it fixes any slowdowns I have more often than not, and it saves me the couple of bucks that I'd spend going out and buying a new device.