Not just Fire Stick issue, but all Kodi installs with third party apps. or worse "builds" on devices with smaller hdd.
The Fire sticks are 8GB before anything is loaded, down to 5.7 or so after Amazon loads their stuff. A typical Kodi install these days may be as high as 600 MB with both addons and user data. Then, something else to watch out for with the Amazon units is the screensaver application(called PHOTOS in the managed applications). That can load an additional 400MB.
So, go to display and screensaver, set to NEVER. Next thing is to regularly delete the cache of all applications by going to Applications, manage installed applications, delete all cache for all Applications, one at a time, DO NOT DELETE THE KODI DATA, only the caches.
Next thing you need is the Raw Maintenance tool(please google for that), and use it EXACTLY per their instruction. After deleting the thumbnails(where most of your memory issues are coming from), you MUST immediately exit and restart Kodi, to install a fresh set of thumbnails.
After doing the above, you will find you have just cleared up to 4GB's of wasted memory space. There is also a program called Clean Master, but to use it with a Fire Stick you'd need a bluetooth mouse or similar to navigate the menu. The way I have outlined here, you will accomplish the same thing, no Bluetooth needed. For regular Android boxes, or Raspberry Pi, etc., things are easier since you are not dealing with Amazons programs and apps, but the basic steps of delete applications cache, and using Raw Maintenance at least once a week for the big "Builds", is still recommended.
You will have no more memory problems as long as you don't go app. crazy.