Flowing on" can be replaced with various synonyms depending on the context. One option is "continuing," which suggests that something is continuing to progress or move forward. "Streaming" is another possible synonym, which implies a smooth and constant flow, like water in a river. "Rolling" can also convey the sense of something moving forward steadily, like a ball rolling down a hill. "Gliding" suggests a graceful and effortless movement, while "slipping" can imply a more furtive or secretive motion. Ultimately, the choice of synonym will depend on the context and the tone that the writer wishes to convey.