You can try removing the app from your Facebook account by going to Facebook > Settings > Apps > Angry Birds Friends > Remove app. Afterwards, you can relaunch it by clicking the link below.
Here are also other tips that may be useful:
- Clear the cache and cookies from your browser
- Check that your firewall or antivirus software is not blocking the game
- Check that you don't have "AdBlocker" or such plug-ins blocking the game
- Try playing the game with a different browser
- Check that you have the latest version of Adobe Flash Player installed
UPDATE September 2018
Starting with Google Chrome version 69 (released on 4th of September), the browser will require you to explicitly enable Flash every single time they want to use it. Chrome will no longer remember this preference between sessions, so every time you use any site that uses Flash, you will have to say “yes, I really want to enable this extension.”
To do this, click on the small padlock next to the address bar and select "Allow" from the Flash menu.