I shall reiterate: there are (or at least, not in my time) badges, flashes etc in the Army that define one's role or specialisation.
As for red tunics, black tunics etc, that comes about as a result of tradition. Centuries of it. And on that basis, the RAF don't come into it. At least, in the Army, nobody went to work dressed like a refugee from a Vaudeville act with gaily coloured badges showing various scenes of aeroplanes in full "whoosh" mode.