Why is it not letting me download Snapchat

Your Apple ID may be disabled, or a parent or guardian has setup which apps you can use. For more information, visit the following articles: If your Apple ID is locked or disabled - Apple Support, Manage App Store purchases, subscriptions, settings, and restrictions on iPhone - Apple Support

You shouldn't need to purchase anything to download Snapchat or any other free app on the App Store. Try editing your billing information to be as accurate as possible, as Apple sometimes requires accounts to have up-to-date information.