All 4 Uses of

flourish

in

Julius Caesar

Whilst bloody treason flourished over us.
p. 129.7 *

flourished = thrived (grew well)

Uses with a meaning too rare to warrant foucs:

[Flourish and shout.]
p. 19.1 *

flourish = fanfare played by trumpets or other horns to announce the entry or exit of royalty

[A crowd of people in the street leading to the Capitol, among them Artemidorus and the Soothsayer. Flourish. Enter Caesar, Brutus, ..., and others.]
p. 93.2

flourish = fanfare played by trumpets to announce the entry or exit of royalty

Definitions:

(1) (flourish as in: the business is flourishing)
to thrive (grow or develop well)
(2) (flourish as in: dismissed them with a flourish)
a showy gesture

or:

the act of waving -- a hand or an item
(3) (meaning too rare to warrant focus)
In Shakespeare's plays, flourish is often used as a stage direction indicating a specific type of showy gesture: fanfare played by trumpets or other horns to announce the entry or exit of royalty.

Check a comprehensive dictionary for other senses including some that are of interest to musicians.