http://www.forbes.com/sites/insertcoin/2014/02/08/flappy-bird-creator-says-hes-taking-the-game-down/
Owner said he's taking down Flappy Bird, more than likely within the next few days.
EDIT: To keep the game, have it already downloaded on your phone. There's no way for it to be deleted from your phone if you already have it downloaded.
If you want it saved, download it to your library in iTunes (for iDevices) so you can always redownload it when you want. I beleive there should be something similar for Android, but I'm not sure since I never used it.