Fire OS is based on Android, so you can install another browser such as Chrome or Firefox from an APK.
If you do not trust APK websites, you can try the insider versions of edge since they let you download APKs directly.
Firefox China allows you to directly download the Firefox APK due to political reasons (RIP Google)
http://www.firefox.com.cn/
Also, you can try installing play store on your tablet:
https://www.howtogeek.com/232726/how...n-fire-tablet/