From Frankish *brand (sword, firebrand) — the connection between fire and sword reflects how a swung blade catches light like a flame.
To wave or flourish something, especially a weapon, as a threat or in triumph; to display ostentatiously.
From Old French brandiss-, stem of brandir (to flourish a sword, to swing a blade), from brand (sword, blade, firebrand), from Frankish *brand, from Proto-Germanic *brandaz (fire, burning brand, a sword). The connection between fire and sword is not metaphorical but material: a sword brandished in battle catches light and flashes — the gleam of a swung blade was likened to fire. The same Proto-Germanic root produced Old English brond or brand (fire, flaming