There are several synonyms for the phrase "fan the flame". Some of these include ignite, kindle, spark, inflame, and stoke. Each of these words carries a slightly different connotation, but all refer to the idea of intensifying or encouraging something. For example, "ignite" might suggest a sudden burst of energy, while "stoke" implies a more deliberate and ongoing effort. Using synonyms like these can help to add variety and nuance to your writing, and can also prevent repetitive word choice. So if you're looking to describe the process of intensifying passion or excitement, consider mixing it up with some of these alternative phrases.