Yes, you can play Cookapps games on multiple devices. Just connect the game to your Facebook account, and you’ll be able to transfer your progress between devices.
However, some game items such as 'Lives', 'Booster' and 'Coin' will be stored on the device. For example, you can not use the lives purchased from the iPhone version on your PC. Only your progress and paid items (jewels, honeys) are synchronized.
Finally, you must be signed in to your Facebook account on your device. Login to Facebook with your mobile browser and log in to Facebook. If you only sign in with the Facebook mobile app, your sync may not work properly.