Due to damaged data not being deleted from the SD card if you have SD card expansion (8GB is not enough space)... a manual deletion of the data on the SD card may be needed... if no SD card ignore...
(This 3.68MB seams to be your SkyID data the app keeps your sign in even if the app is deleted...)
Try Settings > apps and games >manage all apps> Scroll down to sky go... select it.
then select.
clear cache
then clear data
then force stop...
reboot the the kindle tablet (shut down, then restart)
then re-select skygo
go direct to the acoount page in the app and re-sign in that hope fully will reload and store your profile data correctly to the SD card storage...