There are several synonyms that can be used for the phrase "cease to flow". One common word is "stop", which can mean to abruptly come to a halt or to end something. Another synonym is "halt", which can mean to bring something to a stop or to interrupt something that is in progress. "Terminate" is another word that can be used, which means to bring something to an end, often in a formal or final way. "Discontinue" is another possible synonym, which means to stop something permanently or temporarily. Finally, "arrest" can also be used as a synonym, which means to stop something in its tracks or to prevent something from continuing.