In Japanese in a martial arts context: way, manner, style, fashion. A "stream" of transmission, particularly of an old martial arts tradition. Translating this word as school places too many westernized meanings to the word, the process of transmission would not resemble a modern school in most cases.
Derived from 流.
In Chinese this character literally means "stream of water" as in 河深流靜, or other types of stream 氣流 (air current), or metaphorical streams like 意識流 (stream of consciousness). Other Japanese uses of 流 retain this basic meaning.