The flag that has been burned most often is
Russia. Please note, this chart shows percent based on popularity not totals.

As you may or may not know, Google systematically crawls around the web indexing that which it finds to theoretically give you nothing but the best search results. The following chart shows the Googlebot's favorite flags to visit and burn. This is cold, hard fact, although it may or may not reflect on what Googlebot or Google's employees really think.
Please note: I in no way endorse burning real flags (because of the fragile nature of our environment, I can only endorse "burning" pixels!), arson (I only endorse "burning" pixels you own), or any other anti-<insert-your-favorite-country> activities (I only endorse pro-<insert-your-favorite-country> activities) that may or may not be depicted on this website (since the website doesn't favor "burning" one bunch of pixels over another, it might be considered anti-world, but I'm not from another galaxy so nevermind that).