You can download the app to get your coupons by clicking here for the iPhone Apple version, or click here for the Google Android version.
After you download the app you'll need to log in with Facebook or an email account.  To see what Burger King coupons are available, click the Coupons tab.  While you are in a Burger King restaurant, click "Use In-Restaurant" for the coupon you want, or click Mobile Order if you want to order and pay through the app.
Deals may vary by location.  You can find a list of app coupons on the BK Offers Page.