the Heike line; descendants of the Taira clan
Refers to the lineage or descendants of the Taira clan (Heike), often in historical or literary contexts.
He claimed to be a samurai descended from the Heike line.
Compound of 平家 (Heike, the Taira clan) + の (possessive particle) + 流れ (flow, lineage). The term is straightforward and its meaning is transparent from its components.