I am currently running OS 4.5.5.3 on my Kindle fire HDX. I was able to successfully download the Android app apk 5.6.0.14 from here https://www.apkmirror.com/apk/ebay-mobile/ebay/ebay-5-6-0-14-release/ebay-buy-sell-save-money-5-6-0-... and it seems to be working. This update is about a year old but I didn't get a warning that going to blocked from eBay so it should work until a newer version is available in the Amazon app store. You need to go into the settings for applications and turn on the switch to allow apps from unknown sources and delete the old app from your device prior to installation. The newer updates such as those numbered 5.13.x.x or 5.11.x.x would not install on my Kindle. The layout of the application is different from the older one as well but I have no problems navigating through my lists. It has a side bar similar to the Silk browser. Good luck!
