It will appear on the recipient notification screen directly rather than inbox. If recipient accepts the message, then it will be added to inbox.
Use Case: You don't have to worry if your clients have enough storage space on their mobile phones. You can share confidential information, as it wont get stolen along with their phone (even if the phone is lost).
However, in case of sending multiple Flash messages, keep in mind that your users will only be able to see the last message they receive. You cannot include any special characters in Flash message.