'Flourish' in the text is only found twice. In Richard III. 44, 149, 'A flourish, trumpets!—strike alarum, drums!' we have a clear definition of the two terms mentioned: and in Merchant 32, 49, 'even as the flourish when true subjects bow To a new-crowned monarch;" a reference to the principal use of the Flourish, which was to signify the presence of Royal persons.
Trumpets, A trumpet sounds, Trumpet sounded within, Drums and trumpets, Flourish of Trumpets (6 times).
One or other of the above occurs some 51 times in twenty-two plays, either alone, or in connection with Sennet, discharge of cannon, etc. On 18 of these occasions it announces the entrance or presence of a King or Royal personage; 13 times it figures as part of the proceedings in Duels; 10 times signifies the entrance or exit of principal persons, not royal, great generals, etc.; 3 times precedes a public procession, with Royal persons in it; twice it is connected with the advent of Royal Heralds; and once with the arrival of Players (Shrew, Prologue. See also Flourish).
Thus 'Trumpets' divides the honours with 'Flourish' as the mark of Royalty.