Lately, I have searching online to find DotGear's Flappy Bird, and there it was. The real thing.
Step 1: Allowing Apps Install From Unknown Sources
Go to Settings > Apps > Unknown Sources
If it doesn't say this on your device, go to Settings > Security/Privacy and tick the box that says 'Unknown Sources'. You can undo this later if you wish.
Step 2: Getting Flappy Bird
For the Flappy Bird link, click here. You will only be able to access this through a Android tablet or Smartphone. It will come up with a tab at the bottom. Press install. Click the button which says 'Open' as you would like it to install onto you device. There will be two options: Open in File Manager or Package Installer. Press that then press Always. The Apk Installer will appear with all the app info, like it would in the Play Store. Press 'Install', and then it will install on to your device.