Printed electronics using flexible substrates are an emerging area, allowing next generation electronics that can conform and flex with different surfaces, from human skin to in clothing. In the hybrid integration, or sea-of-rigids approach, conventional microchips are mounted onto (generally) plastic substrates such as polyethylene naphthalate (PEN), with (typically) printed silver tracks for interconnections between components. An ongoing research direction is to replace plastic substrates with biodegradable substrates, and to replace silver tracks with non-heavy metal-based tracks. While the substrates and tracks form only part of any overall system, replacing them is a step towards increased sustainability and helps to meet net-zero goals for printed electronic systems. Previously, several papers have investigated printed carbon tracks for low-frequency analog sensing applications. This paper explores the feasibility of using printed carbon tracks on biodegradable substrates for high-frequency sensing applications such as digital signaling over a Serial-Peripheral Interface (SPI). We investigate the printability, thermal stability, and electrical conductivity of carbon ink screen-printed onto six commercially available sustainable and flexible substrates. This includes modeling the connection formed and testing with SPI communications over a range of clock frequencies. We explore multi-layer screen printing to reduce the electrical resistance of the carbon tracks enabling their use in high-frequency SPI communication. This method was evaluated successfully in a custom experimental setup composed of two digital electronic systems connected through a carbon-based flexible connector. Connectors made through two layers of carbon prints allowed short distance SPI communication at a clock frequency of 1 MHz. Connectors of three or more carbon prints allowed SPI communication at clock frequencies up to 16~MHz. The NatureflexTM substrate showed the best overall trade-off in printing versus electronic performance among the sustainable substrates. The results of this study provide guidelines for materials selection and device fabrication for printing onto emerging biodegradable substrates to be used effectively in digital electronic systems.