All 3 Uses of

flourish

in

Frankenstein - 1831 version

One of his most intimate friends was a merchant who, from a flourishing state, fell, through numerous mischances, into poverty.
p. 33.4 *

flourishing = thriving or prospering

In one spot you view rugged hills, ruined castles overlooking tremendous precipices, with the dark Rhine rushing beneath; and on the sudden turn of a promontory, flourishing vineyards with green sloping banks and a meandering river and populous towns occupy the scene.
p. 160.4

flourishing = thriving (growing well)

Clerval desired the intercourse of the men of genius and talent who flourished at this time, but this was with me a secondary object; I was principally occupied with the means of obtaining the information necessary for the completion of my promise and quickly availed myself of the letters of introduction that I had brought with me, addressed to the most distinguished natural philosophers.
p. 163.1

flourished = thrived or prospered

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.