Sideloading Opera Mobile onto the Kindle Fire

First you need to click on the gear on the top right bar to bring up the settings, then click the + more link

Now you want to click on the Device tab.
Next to where it says "allow installation of applications from unknown sources" set that to ON

Then go back to your home screen, and click web.
go to www.handango.com from your silk browser, and search for opera mobile. Click the link when you find it, and it will download the operamobile.apk onto your device. Once the download is complete, click the downloaded apk file and you will then go through the installation process of installing opera mobile onto your kindle fire.