As James mentioned, you might try accessing the Blue Iris mjpg URL directly in your Fire tablet’s browser (eg. outside of SharpTools.io) and double check that the tablet is on the same network as the Blue Iris server.
I usually use the format: http://{blue.iris.ip}:{port}/mjpg/{short_name}
Is that the format you are using?
You may also want to adjust the Blue Iris authentication settings under Web Server → Advanced section → Authentication. I have mine set to "Non-LAN only" which means that I can hit the streams locally without providing any username/password, but if I try to hit it from outside my network, I have to provide the password.