New iPhone 16 on Kindle app (not working)

Hello! Kindle app doesn't want to work on my new iPhone 16! I entered my email and password, got an email with notification, but the app doesn't want to start - instead it says: "Network error - In order to sign in to the Kindle app, you need to be connected to a Wi-Fi or mobile network. Please check your network connection in Settings and try again". Well, I checked the connection and there's absolutly nothing wrong with it! Please, help! I also have an Apple IPAD and works fine on this device..

Many thanks