Network data transmission faces serious privacy and security threats, especially in insecure collaborative networks. One crucial factor is the transmission of shared credentials over public channels. In this paper, we propose a novel continuous covert authentication method CCAuth based on flow watermark to safeguard the privacy of authenticators and enhance the concealment of the authentication process. Diverging from traditional multimedia watermarking techniques, CCAuth requires no alteration of the original data. Instead, it achieves watermark embedding based on the transmission timing of data packets within network flows. Furthermore, it is applicable to diverse transmission scenarios, including videos, audio, images, and more. Theoretical analysis and experimental results demonstrate that CCAuth can effectively enhance the security and concealment of authentication, along with the capacity of covert channels.