It shouldn't. Being a lightweight program, Kodi has no discernible or substantial effect on FireStick's performance. However, the Fire TV Stick's storage is restricted; if most of it has previously been used, you can have performance problems. Getting rid of all the extra files and junk from FireStick memory would be an excellent idea. For instance, to free up space if you've downloaded any third-party applications on your FireStick, be sure to remove the APK files.