Both Uses of

flourish
in
Anne Of Green Gables

It was encircled by huge old willows and tall firs, beneath which flourished flowers that loved the shade.
p. 84.0 *

flourished = thrived

The Debating Club flourished and gave several concerts; there were one or two parties almost verging on grown-up affairs; there were sleigh drives and skating frolics galore.
p. 246.6

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)
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.